The Pride of Econometrician

Senior Project Archive

2011-09-10T01:17:00.001-07:00

http://www.whitman.edu/mathematics/SeniorProjectArchive/

Graphics inclusion

2011-08-24T13:59:00.000-07:00

http://mactex-wiki.tug.org/wiki/index.php?title=Graphics_inclusion

The following is found on wiki:

Including graphics in a LaTeX-document is done with a command like this:

\includegraphics{image.jpg}

where image.jpg is a graphic-file of the JPEG-type. It is assumemed that you have loaded the graphics-package in your preamble. There are variants of this command, for example

\includegraphics[width=0.8\textwidth]{image.jpg}

- see for other options, for example, here or the documentation of the graphics-package. While this is very easy, one needs to be aware that not all file types are supported.

supported file types

These are the file types that are supported, depending on the typesetting-mode you are using. As a Mac-User, you are most likely a user of (pdf)latex with pdf-output.

latex with dvi-output	latex with pdf-output
eps	pdf,jpg,png,mps

See this article in the PracTeX Journal for more on this.

epstopf: including eps-graphics in a pdfLaTeX-document

The epstopf-package helps to overcome the limitations of latex and pdflatex when it comes to available graphic-formats. Its main purpose is to allow the inclusion of .eps-graphic in documents that are typeset in pdflatex (with a pdf as an output file). What the package does is that it calls an external script (with the same name: epstopdf) that converts a eps-graphic into a pdf such that pdflatex can use this. So, if you are using pdflatex, the following document would work:

\documentclass[11pt]{article} \usepackage{graphicx} \usepackage{epstopdf} \begin{document} \includegraphics[width=0.8\textwidth]{image.eps} \end{document}

Add (Hyper-)Links to PDFs

2011-05-13T23:52:00.000-07:00

Add (Hyper-)Links to PDFs

By tom

Source Link: http://texblog.wordpress.com/2007/11/14/hyper-links-to-the-pdfs/

Adding links to PDFs , both internal and external, certainly only makes sense for digital copies of the file. Nevertheless, they still come in handy, for example for actual WWW-addresses or as direct reference inside a document.

Local references

As usual, you first need the package which handles the links:

\usepackage{hyperref}

This does the job for the moment. The package “hyperref” will automatically insert links wherever you place a citation or reference (\cite{}, \ref{}).

Global references

Referencing to URLs or local files can be done as follows:

\href{url}{text}

Try this:

\href{http://texblog.wordpress.com}{\bf{Blog on Latex Matters}}

Colour references

So far, the references were marked by a colour rectangle around them, which is not very appealing (unless you are using Apple Preview). Here is how you remove the border and if you wish define your own colours for references.

Either add this optional argument to the previous package:

\usepackage[colorlinks]{hyperref}

or use a new line and set the colour:

\usepackage{hyperref} \hypersetup{colorlinks}

If you want to define your own colours, you will have to use the latter, as the colours are part of the argument of “hypersetup”. But in order to do so, you first need to define colours, which is why you will need the colour-package:

\usepackage{color}

Then you can define different colours you may want to use for your references, e.g.:

\definecolor{darkred}{rgb}{0.5,0,0} \definecolor{darkgreen}{rgb}{0,0.5,0} \definecolor{darkblue}{rgb}{0,0,0.5}

Latex uses the standard RGB (red/green/blue) colour model. The three values define the intensity for each channel within the interval (just because Latex looks nicer:-).

Now you are ready to use the defined colours, by extending the previously used command:

\hypersetup{ colorlinks, linkcolor=darkblue, filecolor=darkgreen, urlcolor=darkred, citecolor=darkblue }

Note: If your tex-distribution does not contain the hyperref-package, you can download it here (hyperref.zip), including the complete documentation.

WinEdt 6: font changing

2011-04-24T11:46:00.000-07:00

WinEdt 6: font changing

http://comments.gmane.org/gmane.editors.winedt/5662

I'll try to guide you to the new way of changing font settings under WinEdt 6.0, so please go to the following menu:  Options --> Options...  Note the opened left pane and from there select Font Schemes... -> Font  In the opened file select the mentioned 5 lines pertaining to font options;  Click the second (font) button in the upper left corner of the Options panel and select your desired font options;  Now click in the first button to "Load Current Script" and save the new settings. That's all.  You can also change font settings in "private.ini" instead of "font.ini" under "Advanced Configuration" branch of the Options (left) pane.  Good luck!  Bernhard Enders

All Models Are Wrong But Some Are Useful

2011-04-22T11:01:00.001-07:00

“All Models Are Wrong But Some Are Useful” -George Box

George E.P. Box, Robustness in the strategy of scientific model building, page 202 of Robustness in Statistics, R.L. Launer and G.N. Wilkinson, Editors. 1979.

Generalized Information Measures and Their Applications

2011-04-10T16:13:00.000-07:00

Generalized Information Measures
and Their Applications

Inder Jeet Taneja, Ph. D.
Departamento de Matemática
Universidade Federal de Santa Catarina
88.040-900 Florianópolis, SC, Brazil

Chapter 0: Introduction

Chapter 1: Shannon's Entropy

Chapter 2: Information and Divergence Measures

Chapter 3: Entropy-Type Measures

Chapter 4: Generalized Information and Divergence Measures

Chapter 5: M-Dimensional Divergence Measures and Their Generalizations

Chapter 6: Unified (r,s)-Multivariate Entropies

Chapter 7: Noiseless Coding and Generalized Information Measures

Chapter 8: Channel Capacity and Source Coding Theorems

Chapter 9: Statistical Aspects of Information Measures

Chapter 10: Bayesian Probability of Error and Generalized Information Measures

Chapter 11: Fuzzy Sets and Information Measures

Bibliography

About this document ...

Book: Forecasting with Exponential Smoothing The State Space Approach

2011-04-03T12:59:00.000-07:00

Forecasting with Exponential Smoothing
The State Space Approach,Rob Hyndman, Anne Koehler, Keith Ord and Ralph SnyderSpringer Link

Information Theoretic Research

2011-04-02T15:59:00.000-07:00

Information Theory Research Group

at Washington U. St. Louis

Type I or Type II error?

2011-03-11T13:27:00.000-08:00

An interesting discussion with how to memorize these two concepts.

Type I error: false alarm

Type II error: failed detection

Type I and Type II Errors

Posted by Ethan Fosse at March 7, 2011 8:29 PM

Another interesting discussion pointed out by Jeromy Anglim

http://stats.stackexchange.com/questions/1610/is-there-a-way-to-remember-the-definitions-of-type-i-and-type-ii-errors

Fuzzy Least Square Estimation

2011-01-31T10:21:00.000-08:00

Asymptotic properties of least squares estimation with fuzzy observations

Hae Kyung Kim ^,^a^,, Jin Hee Yoon ^a and Ying Li^a

Information Sciences
Volume 178, Issue 2, 15 January 2008, Pages 439-451

Maximum Rank Correlation Estimators

2011-01-29T13:56:00.000-08:00

1. Robert P. Sherman (1993, Econometrica)
The Limiting Distribution of the Maximum Rank Correlation Estimator

2. Aaron K. Han (1987, Journal of Econometrics)
Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator

3. M. G. Kendall (1938, Biometrika)
A New Measure of Rank Correlation

4. Jason Abrevaya (1999, Economics Letters)
Computation of the maximum rank correlation estimator

5. Songnian Chen(2002, Econometrica)
Rank Estimation of Transformation Models

6. Christopher Cavanagh and Robert P. Sherman (1998, Journal of Econometrics)
Rank estimators for monotonic index models

Cosma Rohilla Shalizi

2010-10-23T15:26:00.000-07:00

What a great statistician! And especially for the Notebooks.

Check out
http://www.cscs.umich.edu/~crshalizi/
http://www.cscs.umich.edu/~crshalizi/notebooks/

The Epic Story of Maximum Likelihood

2010-10-22T19:49:00.000-07:00

The Epic Story of Maximum Likelihood
Stephen M. Stigler
Source: Statist. Sci. Volume 22, Number 4 (2007), 598-620.

Institute of Mathematical Statistics Lecture Notes - Monograph Series

2010-10-21T14:25:00.000-07:00

IMS Lecture Notes on Stats.
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&page=past&handle=euclid.lnms

A LaTeX link from MIT

2010-09-18T23:43:00.000-07:00

http://web.mit.edu/rsi/www/pdfs/

Matrix Decomposition

2010-09-09T12:34:00.000-07:00

Matrix Decomposition by Ming Yang at Northwestern U.

The analysis of contingency tables under inequality constraints

2010-07-25T17:19:00.000-07:00

Journal of Statistical Planning and Inference Volume 107, Issues 1-2, 1 September 2002, Pages 45-73

Alan Agresti , , and Brent A. Coull

Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space

2010-07-25T17:18:00.000-07:00

Andrew, 2000, Econometrica

cowles.econ.yale.edu/~dwka/pub/p0994.pdf

Nonlinear Hypotheses, Inequality Restrictions, and Non-Nested Hypotheses

2010-07-22T10:01:00.000-07:00

Nonlinear Hypotheses, Inequality Restrictions, and Non-Nested Hypotheses: Exact Simultaneous Tests i...
Jean-Marie Dufour
Econometrica, Vol. 57, No. 2 (Mar., 1989), pp. 335-355
Published by: The Econometric Society

The Sucess of Econometrics

2010-07-20T10:44:00.001-07:00

The Sucess of Econometrics,
Jan R. Magnus
De Economist; Mar 1999; 147, 1

In Memory of John Denis Sargan

2010-07-19T19:02:00.000-07:00

Econometric Theory
Special Issue devoted to John Denis Sargan

Finite Sample Properties of Bootstrap GMM

2010-07-17T22:08:00.001-07:00

http://interstat.statjournals.net/YEAR/2010/articles/1002002.pdf

The Bootstrap’s Finite Sample Distribution

2010-07-17T22:04:00.000-07:00

http://www.nd.edu/~meg/MEG2004/Marsh-Lawrence.pdf

FINITE SAMPLE APPROXIMATION RESULTS FOR PRINCIPAL COMPONENT ANALYSIS

2010-07-17T21:55:00.000-07:00

http://www.wisdom.weizmann.ac.il/~nadler/Publications/pca_finite_sample_AOS.pdf

Thomas S. Ferguson: BIOGRAPHY

2010-07-09T14:45:00.000-07:00

Biography
Source: F. Thomas Bruss, and Lucien Le Cam, eds. Game theory, optimal stopping, probability and statistics: Papers in honor of Thomas S. Ferguson (Beachwood, OH: Institute of Mathematical Statistics, 2000),

A Course in Large Sample Theory

2010-07-09T13:56:00.000-07:00

A Course in Large Sample Theory
Chapman & Hall, 1996.Table of Contents
Part 1: Basic Probability Theory.
1. Modes of Convergence.
2. Partial Converses.
3. Convergence in Law.
4. Laws of Large Numbers.
5. Central Limit Theorems.
Part 2: Basic Statistical Large Sample Theory
6. Slutsky Theorems.
7. Functions of the Sample Moments.
8. The Sample Correlation Coefficient.
9. Pearson's Chi-Square.
10. Asymptotic Power of the Pearson Chi-Square Test.
Part 3: Special Topics.
11. Stationary m-dependent Sequences.
12. Some Rank Statistics.
13. Asymptotic Distribution of Sample Quantiles.
14. Asymptotic Theory of Extreme Order Statistics.
15. Asymptotic Joint Distributions of Extrema.
Part 4: Efficient Estimation and Testing.
16. A Uniform Strong Law of Large Numbers.
17. Strong Consistency of the Maximum Likelihood Estimates.
18. Asymptotic Normality of the MLE.
19. The Cramer-Rao Lower Bound.
20. Asymptotic Efficiency.
21. Asymptotic Normality of Posterior Distributions.
22. Asymptotic Distribution of the Likelihood Ratio Test Statistic.
23. Minimum Chi-Square Estimates.
24. General Chi-Square Tests

Asymptotic Theory in Probability and Statistics with Applications

2010-07-09T11:12:00.000-07:00

Advanced Lectures in Mathematics, Vol. 2
Asymptotic Theory in Probability and Statistics with Applications
Edited by
Tze Leung Lai (Stanford University)
Lianfen Qian (Florida Atlantic University)
Qi-Man Shao (University of Oregon)

A collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a wide variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is intended for graduate students in probability and statistics, and for researchers in related areas.

Common Features in Economics and Finance

2010-06-25T09:36:00.000-07:00

Common Features in Economics and Finance

Giovanni Urga
Faculty of Finance, Centre for Econometric Analysis, Cass Business School, London EC1Y 8TZ, U.K. (g.urga@city.ac.uk)
This introductory article offers an overview of some developments in the common features literature since the publication of the seminal article by Engle and Kozicki in the Journal of Business & Economic Statistics in 1993, with the aim of highlighting the unifying theme of the contributions in this volume.

Resampling methods in econometrics

2010-06-24T23:36:00.000-07:00

Editors’ Introduction
Resampling methods in econometrics
Jean-Marie Dufoura, b, c, , , and Benoit Perrona, b, c
aCIRANO, Canada
bCIREQ, Canada
cDépartement de sciences économiques, Université de Montréal, Canada
Available online 31 August 2005.

Thirty-five years of journal of econometrics

2010-06-24T21:55:00.000-07:00

By Takeshi Amemiya
Thirty-five years of journal of econometrics
Takeshi Amemiya 1, a,
aDepartment of Economics, Stanford University, Stanford, CA 94035-6072, USA
Available online 13 November 2008.

Inverse Problems in Econometrics

2010-06-23T15:34:00.000-07:00

See a bibligraphy at:
https://www.webdepot.umontreal.ca/Usagers/
carrascm/MonDepotPublic/carrascm/inverse/
inverse.html#IE2-FM

NONPARAMETRIC CURVE ESTIMATION: AN OVERVIEW

2010-06-23T15:28:00.000-07:00

Available at:
ftp://ftp.funep.es/InvEcon/paperArchive/May1997/v21i2a3.pdf

Matrix Algebra in R: Resources, Videos, Textbooks

2010-06-21T23:12:00.000-07:00

Matrix Algebra in R: Resources, Videos, Textbooks

A Brief History of Linear Algebra and Matrix Theory

2010-06-21T22:57:00.000-07:00

A Brief History of Linear Algebra and Matrix Theory
Source: http://darkwing.uoregon.edu/~vitulli/441.sp04/LinAlgHistory.html
The introduction and development of the notion of a matrix and the subject of linear algebra followed the development of determinants, which arose from the study of coefficients of systems of linear equations. Leibnitz, one of the two founders of calculus, used determinants in 1693 and Cramer presented his determinant-based formula for solving systems of linear equations (today known as Cramer's Rule) in 1750. In contrast, the first implicit use of matrices occurred in Lagrange's work on bilinear forms in the late 1700s. Lagrange desired to characterize the maxima and minima of multivariate functions. His method is now known as the method of Lagrange multipliers. In order to do this he first required the first order partial derivatives to be 0 and additionally required that a condition on the matrix of second order partial derivatives hold; this condition is today called positive or negative definiteness, although Lagrange didn't use matrices explicitly.

Gauss developed Gaussian elimination around 1800 and used it to solve least squares problems in celestial computations and later in computations to measure the earth and its surface (the branch of applied mathematics concerned with measuring or determining the shape of the earth or with locating exactly points on the earth's surface is called geodesy. Even though Gauss' name is associated with this technique for successively eliminating variables from systems of linear equations Chinese manuscripts from several centuries earlier have been found that explain how to solve a system of three equations in three unknowns by ''Gaussian'' elimination. For years Gaussian elimination was considered part of the development of geodesy, not mathematics. The first appearance of Gauss-Jordan elimination in print was in a handbook on geodesy written by Wilhelm Jordan. Many people incorrectly assume that the famous mathematician Camille Jordan is the Jordan in ''Gauss-Jordan'' elimination.

For matrix algebra to fruitfully develop one needed both proper notation and the proper definition of matrix multiplication. Both needs were met at about the same time and in the same place. In 1848 in England, J.J. Sylvester first introduced the term ''matrix,'' which was the Latin word for womb, as a name for an array of numbers. Matrix algebra was nurtured by the work of Arthur Cayley in 1855. Cayley studied compositions of linear transformations and was led to define matrix multiplication so that the matrix of coefficients for the composite transformation ST is the product of the matrix for S times the matrix for T. He went on to study the algebra of these compositions including matrix inverses. The famous Cayley-Hamilton theorem which asserts that a square matrix is a root of its characteristic polynomial was given by Cayley in his 1858 Memoir on the Theory of Matrices. The use of a single letter A to represent a matrix was crucial to the development of matrix algebra. Early in the development the formula det(AB) = det(A)det(B) provided a connection between matrix algebra and determinants. Cayley wrote ''There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants.''

Mathematicians also attempted to develop of algebra of vectors but there was no natural definition of the product of two vectors that held in arbitrary dimensions. The first vector algebra that involved a noncommutative vector product (that is, v x w need not equal w x v) was proposed by Hermann Grassmann in his book Ausdehnungslehre (1844). Grassmann's text also introduced the product of a column matrix and a row matrix, which resulted in what is now called a simple or a rank-one matrix. In the late 19th century the American mathematical physicist Willard Gibbs published his famous treatise on vector analysis. In that treatise Gibbs represented general matrices, which he called dyadics, as sums of simple matrices, which Gibbs called dyads. Later the physicist P. A. M. Dirac introduced the term ''bra-ket'' for what we now call the scalar product of a ''bra'' (row) vector times a ''ket'' (column) vector and the term ''ket-bra'' for the product of a ket times a bra, resulting in what we now call a simple matrix, as above. Our convention of identifying column matrices and vectors was introduced by physicists in the 20th century.

Matrices continued to be closely associated with linear transformations. By 1900 they were just a finite-dimensional subcase of the emerging theory of linear transformations. The modern definition of a vector space was introduced by Peano in 1888. Abstract vector spaces whose elements were functions soon followed.

There was renewed interest in matrices, particularly on the numerical analysis of matrices, after World War II with the development of modern digital computers. John von Neumann and Herman Goldstine introduced condition numbers in analyzing round-off errors in 1947. Alan Turing and von Neumann were the 20th century giants in the development of stored-program computers. Turing introduced the LU decomposition of a matrix in 1948. The L is a lower triangular matrix with 1's on the diagonal and the U is an echelon matrix. It is common to use LU decompositions in the solution of a sequence of systems of linear equations, each having the same coefficient matrix. The benefits of the QR decomposition was realized a decade later. The Q is a matrix whose columns are orthonormal vectors and R is a square upper triangular invertible matrix with positive entries on its diagonal. The QR factorization is used in computer algorithms for various computations, such as solving equations and find eigenvalues.

References

S. Athloen and R. McLaughlin, Gauss-Jordan reduction: A brief history, American Mathematical Monthly 94 (1987) 130-142.

A. Tucker, The growing importance of linear algebra in undergraduate mathematics, The College Mathematics Journal, 24 (1993) 3-9.

Mathematical methods for economic theory

2010-06-13T00:11:00.000-07:00

Mathematical methods for economic theory: a tutorialby Martin J. Osborne
from University of Toronto

Engeneering Statistics Handbook

2010-06-09T15:47:00.000-07:00

A nice reference for statistics at
http://www.itl.nist.gov/div898/handbook/index.htm

R: Probit Model

2010-04-23T15:17:00.000-07:00

Here is an example from the internet,

# Simulate from probit model --
simulate <- function(N) {x1 <- 2*runif(N)
x2 <- 5*runif(N) ystar <- 7 + 3*x1 - 4*x2 + rnorm(N)
y <- as.numeric(ystar>0)
print(table(y))
data.frame(y, x1, x2, ystar)}

> # A simple example of estimation --
> D <- simulate(200)y0 197 103
> m <- glm(y~x1+x2, family=binomial(probit), data=D)

> summary(m)
Call:
glm(formula = y ~ x1 + x2, family = binomial(probit), data = D)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.125e+00 -7.332e-04 2.107e-08 7.812e-04 2.326e+00
Coefficients:
Estimate Std. Error z value Pr(>z)(Intercept)
8.0810 1.6723 4.832 1.35e-06 ***x1 3.1877 0.6948 4.588 4.47e-06 ***x2 -4.4544 0.8488 -5.248 1.54e-07 ***
---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(Dispersion parameter for binomial family taken to be 1)
Null deviance: 277.079 on 199 degrees of freedom
Residual deviance: 40.845 on 197 degrees of freedom
AIC: 46.845

Number of Fisher Scoring iterations: 10

For this one dataset of 200 observations, we got back estimate which is quite close to the true .

Let us look at how well this model predicts in-sample:
> # Predictions using the model --
> predictions <- predict(m)
> summary(predictions)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-13.0800 -4.1720 0.1780 0.3705 5.1250 12.7400
> yhat <- ifelse(predictions>0, 1, 0)
> table(yhat, D$y)

It does pretty well. For 93 cases, the truth is 0 and the predicted value is0. Similarly, for 98 cases, the truth is 1 and the predicted value is 1. There are only 9 cases which are misclassified.

Music Gallery

2010-04-13T15:07:00.000-07:00

Last Updated : Mar 23, 2011

Are you the one? --- Timmo Tolkki

As Love Is My Witness --- Westlife

Bad Day --- By Daniel Powter

Beauty and Beast --- Celine Dion

Because You Loved Me --- Celine Dion

Big Girls Don't Cry --- Fergie

Born to Make you Happy --- Britney Spears

Can you feel the love tonight? --- Elton John

Can't Get Over You --- September

Casablanca --- Bertie Higgins

Complicated --- Avril Lavigne

Don't Be Stupid --- Shania Twain

Don't Go Away --- BY2 (Chinese Version)

Don't Go Away --- BY2 (English Version)

Don't Impress Me Much --- Shania Twain

(Everything I Do) I Do It For You --- By Bryan Adams

Everytime --- Britney Spears

Eyes on Me --- Celine Dion

Falling for You --- Colbie Caillat

From This Moment On --- Shania Twain

Fuckin' Perfect --- Pink (P!nk)

Girlfriend --- Avril Lavigne

God Is a Girl --- Groove Coverage

Heaven Love --- Ying Wang (Chinese)

How Do I Live --- Leanne Rimes

How Have You Been --- S.H.E. (Chinese)

Hui Hu Xi de Tong --- Jinru Liang (Chinese)

I'm Your Angel --- Celine Dion and R. Kelly

I'm Yours ---- Jason Mraz

I'll be There for You ---- Rembrandts

I Love You --- S.H.E. (Chinese)

I see you --- Leona Lewis

I Surrender --- Celion Dion

I Wanna Know What Love Is --- Mariah Carey

I Will Always Love you --- Whitney Houston

If That's What Takes --- Celine Dion

It's All Coming Back To Me Now --- Celine Dion

K-Lovers --- Pin and Liang (Chinese)

Love Story --- Taylor Swrift

Loving Loving You --- Rene Liu (Chinese)

Lucky --- Jason Mraz and Colbie Caillat

Make It Possible --- By Xiaoming Huang (Chinese)

Miracle ---- Celine Dion

Missing You (Heart-Broken) --- Jie Xu (Chinese)

Missing You Suddenly --- Youjia Lin (Chinese)/Originally by Wuyuetian

My Heart Will Go On --- Celine Dion

Need You now --- Lady Antebellum

Nobody But You --- Wonder Girls

Only Love ---- By Trade Marks

Our Song --- Taylor Swift

Realize ---- By Colbie caillat

Shadows --- Westlife

She's Gone --- Steel Heart

That's the Way it is! --- Celine Dion

The Power of Love --- Celine Dion

There you'll be ----Faith Hill

To Love Your More --- Celine Dion

Truly Madly Deeply --- Savage Garden

U Make Me Wanna --- By Blue-in-one

Up --- Shania Twain

Wait For You --- Elliott Yamin

What About Now --- Westlife

When A Man Loves A Woman --- Michael Bolton

What Happen To Us --- S.H.E. (Chinese)

When I Fall in Love --- Celine Dion

When I need You --- Celine Dion

When You're Gone --- Avril Lavigne

Where We Are --- Westlife

You and I --- Celine Dion

You and I Both --- Jason Mraz

You Belong With Me --- Taylor Swift

You're not Alone --- Michael Jackson

You're Still the One! --- Shania Twain

You Raise Me Up --- Josh Groban

You've Got A Way --- Shania Twain

A New Era: A Beautiful Mind

2010-04-12T13:20:00.000-07:00

Look at this guy, who is changing this world in a way beyond your imagination. This world is so beautiful, because of beautiful minds as such that are on the way to make it perfect. Be creative and be valuable to the world. Make a change from now on, in a better way!

The MIT Genius
http://v.youku.com/v_show/id_XMTQ0MTM5Njg0.html

R: Linear Regression Example of Faraway (2002)

2010-04-08T00:19:00.000-07:00

See pp.23 of Faraway (2002), Practical Regression and Anova using R at:
http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf

> data(gala)
> gala
> gfit <- lm(Species ˜ Area + Elevation + Nearest + Scruz + Adjacent,data=gala)
> summary(gfit)

The following is to compute some statistics by writing R code, just for illustrative purpose (since these estimates are already computed by the function lm())

> x <- cbind(1,gala[,-c(1,2)])
> y <- gala$Species
> t(x) %*% x
Error: %*% requires numeric matrix/vector arguments

> x <- as.matrix(x)
> t(x) %*% x
> xtxi <- solve(t(x) %*% x)
> xtxi

># Get it using lm()
> gfit <- lm(Species ˜ Area + Elevation + Nearest + Scruz + Adjacent,data=gala)
> gs <- summary(gfit)
> gs$cov.unscaled
> names(gs)
> names(gfit)
> gfit$fit
> gfit$res

>#Get beta_hat by
> xtxi %*% t(x) %*% y #or
> solve(t(x) %*% x, t(x) %*% y)

> sqrt(sum(gfit$resˆ2)/(30-6))
> sqrt(diag(xtxi))*60.975
> #R^2
> 1-sum(gfit$resˆ2)/sum((y-mean(y))ˆ2)

R: replacing for loop by apply

2010-04-05T21:17:00.000-07:00

The function "apply" in R can help to save a lot computational time when it is replacing for loops. The following is just an example illustrating this point.

time1=proc.time()
I=50;B=50;x=matrix(0,nrow=I,ncol=B);
for (i in 1:I){
for (b in 1:B){ x=matrix(rnorm(2500),nrow=50); eigen(x) }
}
time1=proc.time()-time1

time2=proc.time()
I=matrix(1:50,nrow=1); B=matrix(1:50,nrow=1);
eig2<-function(x1=1){
x=matrix(rnorm(2500),nrow=50);
eigen(x);
}
eig1<-function(x2=1){apply(B,1,eig2); }
apply(I,1,eig1);time2=proc.time()-time2
time1time2

#> time1
# user system elapsed
# 20.62 0.11 20.97
#> time2
# user system elapsed
# 0.07 0.11 0.17

A plot example

2010-04-04T14:31:00.000-07:00

This example is taken from “Introduction to the R Project for Statistical Computing for Use at the ITC” by David Rossiter, pp.133, http://cran.r-project.org/doc/contrib/Rossiter-RIntro-ITC.pdf

n <- 30; mu <- 180; sd <- 20; bin.width <- sd/3v <- rnorm(n, mu, sd)
hist(v, breaks = seq(mu-5*sd, mu+5*sd, by=bin.width))
points(x, dnorm(x, mu, sd)*(n*bin.width))

### visualise the variability of small random samples
# sample size
n <- 30
# number of plot rows, columns
rows <- 2; cols <- 2;
reps <- rows*cols
# parameters of the normal distribution
mu <- 180; sd <- 20
# set up graphic display
par(mfrow=c(rows, cols))
# number of s.d.'s for histogram displays
dd <- 3.5
# compute bin width from s.d and
# the number of bars for each
bin.width=sd/3
# scale x-axis
x.min <- mu-(sdd*sd); x.max <- mu+(sdd*sd)
# scale y-axis
y.max <- n*0.5*bin.width/sd

# compute and display each graph
for (i in 1:reps)
{
v <- rnorm(n, mu, sd)
hist(v, xlim=c(x.min,x.max),
ylim=c(0, y.max),breaks = seq(mu-5*sd, mu+5*sd, by=bin.width),
main="", xlab=paste("Sample",i)) ;
x <- seq(x.min, x.max, length=120)
# true normal distribution
points(x,dnorm(x, mu, sd)*(n*bin.width),type="l", col="blue", lty=1, lwd=1.8)
# distribution estimated from sample
points(x,dnorm(x, mean(v), sd(v))*(n*bin.width),type="l", col="red", lty=2, lwd=1.8)
# print sample params.
# and Pr(Type I error)
text(x.min, 0.9*y.max, paste("mean:", round(mean(v),2)),pos=4)
text(x.min, 0.8*y.max, paste("sdev:", round(sd(v),2)),pos=4)
text(x.min, 0.7*y.max,paste("Pr(t):", round((t.test(v, mu=mu))$p.value,2)),pos=4)
}

# clean up
par(mfrow=c(1,1))
rm(n, rows, cols, reps, mu, sd, v, i, sdd, bin.width, x.min, x.max, y.max, x)

tapply for aggregate statistics

2010-04-04T14:21:00.000-07:00

The use of apply function can avoid a for loop and it leads to faster computing. This example is about how to use tapply to compute some group/aggregated statistics.

Use tapply for most basic by processing (By processing = Aggregate statistics = stratified estimates; statistics computedafter cross-classifying data)

> y <- 1:8
> sex <-c(rep(’male’,4),rep(’female’,4))
> treat <-rep(c(’A’,’B’),4)
> sex
[1] "male" "male" "male" "male" "female" "female" "female" "female"
> treat
[1] "A" "B" "A" "B" "A" "B" "A" "B"
> tapply(y, sex, mean)
female male
6.5 2.5
> tapply(y, treat, mean)
A B
4 5
> tapply(y, list(sex,treat), mean)
A B
female 6 7
male 2 3

Subsetting data frame in R

2010-04-04T14:02:00.000-07:00

The following is taken from “Statistical Computing and Graphics Course Notes” by Frank E. Harrell. http://cran.r-project.org/doc/contrib/Harrell-statcomp-notes.pdf

> # Subset a simple vector
> x1 <- 1:4
> sex <- rep(c(’male’,’female’),2)
> subset(x1, sex==’male’)
[1] 1 3

> # Subset a data frame
> d <- data.frame(x1=x1, x2=(1:4)/10, x3=(11:14), sex=sex)
> d
x1 x2 x3 sex
1 1 0.1 11 male
2 2 0.2 12female
3 3 0.3 13 male
4 4 0.4 14 female

> subset(d, sex==’male’)
x1 x2 x3 sex
1 1 0.1 11 male
3 3 0.3 13 male

> subset(d, sex==’male’ & x2>0.2)
x1 x2 x3 sex
3 3 0.3 13 male

> subset(d, x1>1, select=-x1)
x2 x3 sex
2 0.2 12 female
3 0.3 13 male
4 0.4 14 female

> subset(d, select=c(x1,sex))
x1 sex
1 1 male
2 2 female
3 3 male
4 4 female

> subset(d, x2<0.3, select=x2:sex)
x2 x3 sex
1 0.1 11 male
2 0.2 12 female

> subset(d, x2<0.3, -(x3:sex))
x1 x2
1 1 0.1
2 2 0.2

> attach(subset(d, sex==’male’ & x3==11, x1:x3))

Text Processing using LaTeX

2010-04-02T16:49:00.000-07:00

Learning LaTex from Cambridge at http://www-h.eng.cam.ac.uk/help/tpl/textprocessing/LaTeX_intro.html

R: snow Simplified

2010-04-02T16:05:00.000-07:00

The 'snow' package provides a high-level interface for using a workstation cluster for parallel computations in R. Here is a friendly user guide, made by Sigal Blay (sblaysfu.ca).

http://www.sfu.ca/~sblay/R/snow.html

the following is the txt file:

snow Simplified
~~~~~~~~~~~~~~~
Many computationally demanding statistical procedures, such
as Bootstrapping and Markov Chain Monte Carlo, can be speeded
up significantly by using several connected computers in
parallel.
The package snow (an acronym for Simple Network Of
Workstations) provides a high-level interface for using a
workstation* cluster** for parallel computations*** in R.
snow relies on the Master / Slave model of communication in
which one device or process (known as the master) controls
one or more other devices or processes (known as slaves).
In Los Angeles, officials pointed out that such terms as
"master" and "slave" are unacceptable and offensive, and
equipment manufacturers were asked not to use these terms.
Some manufacturers changed the wording to primary / secondary
(Source: CNN).
snow Simplified is an adaptation of an article by Anthony
Rossini, Luke Tierney and Na Li, 'Simple parallel statistical
computing in R'.
It has been made by Sigal Blay ( http://www.sfu.ca:/~sblay ).
This work has been made possible by the Statistical Genetics
Working Group at the Department of Statistics and Actuarial
Science, SFU.
-----------------------------------------------------------------
snow implements an interface to three different low level
mechanisms for creating a virtual connection between processes:
Socket
PVM (Parallel Virtual Machine)
MPI (Message Passing Interface)
--- Starting and Stopping clusters ---
The way to Initialize slave R processes depends on your system
configuration. If MPI is installed and there are two computation
nodes, use:
> cl <- makeCluster(2, type = "MPI")
Shut down the cluster and clean up any remaining connections
between machines:
> stopCluster(cl)
--- clusterCall(cl, fun, ...) ---
cl: the computer cluster created with makeCluster.
fun: the function to be applied.
clusterCall calls a specified function with identical arguments
on each node in the cluster.
The second argument is a function object.
The arguments to clusterCall are evaluated on the master,
their values transmitted to the slave nodes which execute the
function call.
> myfunc <- function(x=2){x+1}
> myfunc_argument <- 5
> clusterCall(cl, myfunc, myfunc_argument)
is the same as
> clusterCall(cl, function(x=2){x+1}, 5)
and the result:
[[1]]
[1] 6
[[2]]
[1] 6
--- clusterEvalQ(cl, expr) ---
cl: the computer cluster created with makeCluster.
expr: an expression, typically a function call.
clusterEvalQ evaluates a literal expression on each cluster node.
'expr' is treated on the master as a character string.
The expression is evaluated on the slave nodes.
Finding the host name for each cluster node:
> clusterEvalQ(cl, Sys.getenv("HOST"))
[[1]]
HOST
"stat-db"
[[2]]
HOST
"stat-db1"
Loading the boot package on all cluster nodes:
> clusterEvalQ(cl, library(boot))
clusterEvalQ is the cluster version of the R function 'evalq'.
--- clusterApply(cl, seq, fun, ...) ---
clusterApply takes a cluster, a sequence of arguments (can be a
vector or a list), and a function, and calls the function with
the first element of the list on the first node, with the second
element of the list on the second node, and so on. The list of
arguments must have at most as many elements as there are nodes
in the cluster.
> clusterApply(cl, 1:2, sum, 3)
[[1]]
[1] 4
[[2]]
[1] 5
--- clusterApplyLB(cl, seq, fun, ...) ---
clusterApplyLB is a load balancing version of clusterApply.
It hands in a balanced work load to slave nodes when
the length of seq is greater than the number of cluster nodes.
Doesn`t work if cluster Type=Socket.
> length(cl)
[1] 2
> clusterApplyLB(cl, 1:3, sum, 3)
[[1]]
[1] 4
[[2]]
[1] 5
[[3]]
[1] 6
Using clusterApplyLB can result in better cluster utilization
than using clusterApply. However, increasing communication can
reduce performance. Furthermore, the node that executes a
particular job is nondeterministic, which can complicate
ensuring reproducibility in simulations.
--- clusterExport(cl, list) ---
Assigns the global values on the master of the variables named in
list to variables of the same names in the global environments of
each node.
> myvar <- 666
> clusterExport(cl, "myvar")
--- clusterSplit(cl, seq) ---
clusterSplit splits seq into one consecutive piece for each
cluster and returns the result as a list with length equal to the
number of cluster nodes. The pieces are chosen to be close to
equal in length.
> clusterSplit(cl, 1:6)
[[1]]
[1] 1 2 3
[[2]]
[1] 4 5 6
--- parApply(cl, X, MARGIN, fun, ...) ---
X: the array to be used.
MARGIN: a vector giving the subscripts which the function will be
applied over. '1' indicates rows, '2' indicates columns,
'c(1,2)' indicates rows and columns.
fun: the function to be applied.
parApply is the parallel version of `the R function apply.
A<-matrix(1:10, 5, 2)
> A
[,1] [,2]
[1,] 1 6
[2,] 2 7
[3,] 3 8
[4,] 4 9
[5,] 5 10
> parApply(cl, A, 1, sum)
[1] 7 9 11 13 15
--- parRapply(cl, X, fun, ...) ---
row parallel 'apply' function for matrix X.
May be slightly more efficient than parApply.
--- parCapply(cl, X, fun, ...) ---
Column parallel 'apply' function for matrix X.
May be slightly more efficient than parApply.
--- parLapply(cl, X, fun, ...) ---
parLapply is the parallel version of the R function 'lapply'.
'lapply' returns a list of the same length as 'X'. Each element
of which is the result of applying 'fun' to the corresponding
element of 'X'.
Create a list of two sequences of numbers:
> x <- list(alpha = 1:10, beta = exp(-3:3))
> x
$alpha
[1] 1 2 3 4 5 6 7 8 9 10
$beta
[1] 0.04978707 0.13533528 0.36787944 1.00000000 2.71828183
[7] 7.38905610 20.08553692
Calculate quantiles for each sequence - parLapply returns a list:
> parLapply(cl, x, quantile)
$alpha
0% 25% 50% 75% 100%
1.00 3.25 5.50 7.75 10.00
$beta
0% 25% 50% 75% 100%
0.04978707 0.25160736 1.00000000 5.05366896 20.08553692
--- parSapply(cl, X, fun, ..., simplify=TRUE, USE.NAMES=TRUE) ---
parSapply is the parallel version of `the R function 'sapply'.
'sapply' is a "user-friendly" version of 'lapply'.
It returns a vector or matrix with 'dimnames' if appropriate.
Calculate quantiles for each sequence - parSapply returns a matrix:
> parSapply(cl, x, quantile)
alpha beta
0% 1.00 0.04978707
25% 3.25 0.25160736
50% 5.50 1.00000000
75% 7.75 5.05366896
100% 10.00 20.08553692
--- parMM(cl, A, B) ---
parMM performs parallel matrix multiplication.
A, B are the matices to be multiplied.
--- How much faster is using snow? ---
To compare performace, use the command system.time().
Here is an example:
Create a matrix of random normaly distributed numbers:
> A <- matrix(rnorm(1000000), 1000)
Check CPU time for unparallel matrix multiplication:
> system.time(A %*% A)
[1] 5.33 0.02 5.36 0.00 0.00
elapesed time was 5.36 seconds
... And for parallel matrix multiplication:
> system.time(parMM(cl, A, A))
[1] 2.49 2.09 9.16 0.00 0.00
elapsed time was 9.16 seconds.
Even in dedicated clusters with high speed networking,
communication is orders of magnitude slower than computation.
In order to reduce communication costs, eliminate unnecessary data
transfer.
--- Random Number Generation ---
The default random number generators are likely to be correlated:
> clusterCall(cl, runif, 3)
[[1]]
[1] 0.4960831 0.5095497 0.2971236
[[2]]
[1] 0.4960831 0.5095497 0.2971236
A way of addressing this is random seeding:
clusterApply(cl, runif(cl, max=100000), set.seed)
References:
Rossini, A., Tierney, L., and Li, N. (2003). Simple parallel
statistical computing in R. UW Biostatistics working paper series,
Paper 193, University of Washington.
http://www.bepress.com/uwbiostat/paper193.
Tierney, L., Rossini, A., Li, N., and Sevcikova, H. (2004).
The snow Package: Simple Network of Workstations. Version 0.2-1.
http://cran.r-project.org/doc/packages/snow.pdf
--------------------------------------------------------------------
Workstation - A workstation is a computer intended for individual
use that is faster and more capable than a personal computer.
i.e. have a faster microprocessor, a large amount of random access
memory (RAM), and special features such as high-speed graphics
adapters.
Source: whatis.com
http://whatis.techtarget.com/
Cluster - In a computer system, a cluster is a group of servers
and other resources that act like a single system and enable high
availability and, in some cases, load balancing and parallel
processing.
Source: whatis.com
http://whatis.techtarget.com/
Parallel Computing / Parallel Processing -
The simultaneous use of more than one computer to execute a program.
Objectives: scalability - the capability to hadle larger workloads
reducing execution time
Source: bitpipe
http://www.bitpipe.com/

Matlab is Great; R is Exciting!

2010-04-02T15:18:00.000-07:00

Preparing for the tutorial of "Introductory Econometrics with Examples in R" gets me really excited about it. R is a very powerful language (some body claim that it is only an environment, which is the case when you only use built-in functions or packages available. It actually can do more than that, much much more.) It can do whatever you can imagin, e.g. solving equations, optimization, numerical integration, monte carlo, statistical inference, Bayesian analysis, MCMC, bootstrap, EN, Sparse PCA, time series analysis, panel data, spatial analysis, production analysis, graphical analysis, animation, clustering, parrallel computing, .... It can also do many things that you cannot even imagin, such as Archetypal Analysis, fuzzy knowledge base learning, Forensic Genetics, etc. Just check the online packages at
http://cran.r-project.org/index.html

Getting excited, I've decided to write/collect one example here per day to keep practicing and learning R. Hope this will continue as a habit and attract interested readers as well.

Degrees of Freedom

2010-02-12T23:23:00.000-08:00

Not clear about the concept of degrees of freedom? That's not embarassed at all, since many professors/book writers are not clearly defining them either. Read the following article by I.J. Good on American Statistician to clear the cloud.

The American Statistician, Vol. 27, No. 5 (Dec., 1973), pp. 227-228

Prior information

2010-02-10T17:10:00.001-08:00

Making use of prior information in economic modelling serves as a major role in improving the predictability of economic models and its role in economic analysis. Nevertheless, prior information, which is usually not from the observed sample, is subjected to mispecification. Therefore, a valid test of this nonsample information using available sample deserves particular attention.

Hypothesis testing on prior in the form of equality constraints has a long history, dating back to 1920s by the work of Theil, Wald, Pearson, Newyman, etc. The test on inequality constraints starts in the statistics literature by Walat (1987 JASA, 1988 BKA, 1989 JoE), who transform the testing problem to be the one-sided hypothesis testing framework. Results of Kudo, Perlman, Nuesch, etc. were applied to derive the asymptotic/exact distributions of the LR, W, KT statistics. These statistics are shown to be (asymptotically) equivalent and have a distribution charactorized by a weighted sum of independent chi-squared distributions.

Testing inequality constraints has its own difficulty since the constrained estimator does not have an explicit expression as the original data matrix. The derivation of the test statistic needs finding a least favorable value of the parameter of interest. It turns out that the constraint imposed will be equality and those unbinding ones are not imposed.

Testing inequality constraints still has a long way to go, given its rather complexity. Yet, a lot of time economic priors come in the form of inequality. For example, the MPC is in between 0 and 1. The production function is increasing and concave, i.e. the first derivative is positive and the second derivative is negative. Equity premium should increase in some economic ratios, such as earning price ratiro, book to market ratio, etc. Given these examples, it is urgent to develop some convincing testing procedures that can accomodate all kinds of inequality prior information validation.

Mankiw on Bernanke

2010-01-17T13:39:00.000-08:00

See Economic view by Mankiw at NYT.

Gelman on Efron: Bayesian statistics

2010-01-17T13:34:00.001-08:00

Andrew Gelman post a blog on the article of Efron and Kass to appear on Journal of Statistical Science. See the interesting discussion here.

Monetary Policy and Asset Bubbles in 2010

2010-01-13T09:53:00.000-08:00

Guest Contribution: Monetary Policy and Asset Bubbles in 2010 at EconBrowser
By Joseph E. Gagnon

Video: Challenging Bernanke on Housing Bust

2010-01-13T09:49:00.000-08:00

Click VIDEO at Real Time Economics Economic insight and analysis from The Wall Street Journal.

Lars Hansen: Macroeconomic Risk

2010-01-12T23:36:00.000-08:00

Beliefs, Doubts and Learning: Valuing Macroeconomic Risk
Author(s): Lars Peter Hansen 1
doi: 10.1257/aer.97.2.1

View PDF article (572 K)

An Interview with Lars Hansen

2010-01-12T23:33:00.000-08:00

“An Interview with Lars Hansen”.
Eric Ghysels and Alistair Hall, eds. Journal of Business Economic Statistics

World Economy 2010: Better or Worse?

2010-01-10T15:30:00.000-08:00

See 2010 Predictions From Shiller, Blinder, Rajan and More for some opinions shared by Economists at AEA anual's meeting in Atlanta.

Lousy Investment in Housing Market?

2010-01-10T15:28:00.000-08:00

Some opinions on investment on a house are reflected by Fed Economist: Housing Is a Lousy Investment

Personal Credit Crisis of An Economist

2010-01-10T14:29:00.000-08:00

See My Personal Credit Crisis by EDMUND L. ANDREWS

Complexity of Macroeconomics

2010-01-10T14:05:00.000-08:00

See Accountability? at Mankiw's blog.

A blog on Latex and related issues

2009-10-29T01:38:00.000-07:00

Read here

A Beamer Quickstart

2009-10-29T01:25:00.000-07:00

A Beamer Quickstart
by
Rouben Rostamian
December 2004

Residue Theorem and Its Application

2009-10-23T09:48:00.000-07:00

See Wikipedia, http://en.wikipedia.org/wiki/Residue_theorem
The residue theorem and its applications by Oliver Knill:
http://www.math.harvard.edu/~knill/teaching/residues_1996/residue.pdf

STATISTICS: REFLECTIONS ON THE PAST AND VISIONS FOR THE FUTURE

2009-10-20T10:25:00.000-07:00

STATISTICS: REFLECTIONS ON THE PAST AND VISIONS FOR THE FUTURE
Author: C. Radhakrishna Rao a
Affiliation:
a Pennsylvania State University, PA, U.S.A.
DOI: 10.1081/STA-100107683
Publication Frequency: 20 issues per year
Published in: Communications in Statistics - Theory and Methods, Volume 30, Issue 11 November 2001 , pages 2235 - 2257
Formats available: HTML (English) : PDF (English)

Multivariate t-distribution

2009-10-17T12:29:00.000-07:00

See Wikipedia

Central Limit Theorem

2009-10-14T10:11:00.000-07:00

Papers on Central Limit Theorem on Project Euclid

Law of Large Numbers

2009-10-14T10:09:00.000-07:00

Papers on Law of Large Numbers on ProjectEuclid.

Bootstrap: Collection in Statistical Sicence (2003)

2009-10-12T22:42:00.000-07:00

Statistical Science
A Review Journal of The Institute of Mathematical Statistics.
Volume 18, Issue 2
Publication Date: May 2003

On readings R. A. Fisher

2009-10-12T10:56:00.000-07:00

On Reading R.A. Fisher,
By Leonard J. Savage
Annals of Statistics, 1976, Vol 4, No 3, 441-500

Boosting

2009-10-10T11:06:00.000-07:00

''Boosting is a general method of producing a very accurate prediction rule by combining rough and moderately inaccurate "rules of thumb." Much recent work has been on the "AdaBoost" boosting algorithm and its extensions. ''
Click the above link to see references.

Bayesian Econometrics Methods

2009-10-07T18:30:00.000-07:00

Bayesian Econometric Methods
By Koop, Poirier and Tobias, 2007

Markov Chain Monte Carlo (1)

2009-10-07T13:26:00.000-07:00

Understanding the Metropolis-Hastings Algorithm
Author(s): Siddhartha Chib and Edward Greenberg
Source: The American Statistician, Vol. 49, No. 4 (Nov., 1995), pp. 327-335
Published by: American Statistical Association
Stable URL: http://www.jstor.org/stable/2684568

Explaining the Gibbs Sampler
George Casella; Edward I. George
The American Statistician, Vol. 46, No. 3. (Aug., 1992), pp. 167-174.Stable URL:http://links.jstor.org/sici?sici=0003-1305%28199208%2946%3A3%3C167%3AETGS%3E2.0.CO%3B2-R

Mathworks: Matlab tutorial

2009-09-29T23:04:00.000-07:00

MATLAB Tutorial
Choose a MATLAB tutorial or other resource that matches your learning style.

MATLAB Tutorial Files
CEE Course Support

R: Getting started

2009-09-29T22:48:00.000-07:00

R: Getting started

CRAN NOTES:Contributed Documentation

Superpc for R: Tutorial

2009-09-29T22:27:00.000-07:00

Superpc for R: Tutorial

The methodology is described in the papers: Semi-supervised methods for predicting patient survival from gene expression papers (Bair, Tibshirani) PLOS Prediction by supervised principal components (Bair, Hastie, Paul, Tibshirani) Stanford tech report

Statistical Computing with R (2)

2009-09-29T22:07:00.000-07:00

MAT 356 R Tutorial, Spring 2004
Statistical Computing with R

R Tutorial

Statistics with R

A Quick, Painless Tutorial and Reference on the R Statistical Package

Time Series Analysis and Its Applications: With R Examples

R Tutorial_Clarkson University

2009-09-29T22:03:00.000-07:00

R Tutorial
Clarkson University
Dept. of Mathematics

Springer Texts in Statistics

2009-09-27T11:26:00.000-07:00

Springer Texts in Statistics
ISSN
1431-875X
SpringerLink Date
Thursday, March 16, 2006

Create your own history

2009-09-23T18:20:00.001-07:00

Rama is the prince of this blog, who passed the field exam on Sep 1, the cumulative exam on Sep 11, and oral defence today, Sep 23. He motivates us to create our own history and vividly tells us a story that "everything is possible, hardworking making it!"

Notation in Econometrics

2009-09-22T13:43:00.000-07:00

Notation in econometrics: a proposal for a standard
Authors: Abadir, Karim; Magnus, Jan1
Source: The Econometrics Journal, Volume 5, Number 1, June 2002 , pp. 76-90(15)
Publisher: Blackwell Publishing

MATRIX ALGEBRA

2009-09-22T13:09:00.000-07:00

Title:
MATRIX ALGEBRA, by Karim M. Abadir and Jan R. Magnus, Cambridge University Press, 2005
Source:
Econometric Theory [0266-4666] Otsu, Taisuke (2006) volume: 22 issue: 5 page: 968 -972

Glance at Advanced Statistics: Linear Regression

2009-09-22T10:38:00.000-07:00

Advanced Statistics: Linear Regression

Title:
Advanced Statistics: Linear Regression, Part I: Simple Linear Regression
Source:
Academic Emergency Medicine [1069-6563] Marill (2004) volume: 11 page: 87 -93

Title:
Advanced Statistics: Linear Regression, Part II: Multiple Linear Regression
Source:
Academic Emergency Medicine [1069-6563] Marill (2004) volume: 11 page: 94 -102

40 Puzzles and Problems in Probability and Mathematical Statistics

2009-09-22T10:30:00.000-07:00

40 Puzzles and Problems in Probability and Mathematical Statistics

SpringerLink Book series
Problem Books in Mathematics

Digest of Education Statistics

2009-09-22T09:55:00.000-07:00

Digest of Education Statistics
By National Center for Education Statistics
Annual Reports Program

Scientific Computing with MATLAB and Octave

2009-09-22T09:41:00.000-07:00

Scientific Computing with MATLAB and Octave

SpringerLink Book Series
Texts in Computational Science and Engineering

Myopic Loss Aversion and the Equity Premium Puzzle

2009-09-07T11:40:00.000-07:00

Benartzi, Shlomo; Richard H. Thaler (February 1995).
"Myopic Loss Aversion and the Equity Premium Puzzle".
The Quarterly Journal of Economics 110 (1): 73–92.

"The Equity Premium Puzzle in Retrospect".

2009-09-07T11:20:00.001-07:00

Mehra, Rajnish; Edward C. Prescott (2003).
"The Equity Premium Puzzle in Retrospect".
in G.M. Constantinides, M. Harris and R. Stulz. Handbook of the Economics of Finance. Amsterdam: North Holland. pp. 889–938.

"The Equity Premium: It's Still a Puzzle"

2009-09-07T11:19:00.000-07:00

Kocherlakota, Narayana R. (March 1996).
"The Equity Premium: It's Still a Puzzle" (PDF).
Journal of Economic Literature 34 (1): 42–71. http://www.econ.ucdavis.edu/faculty/kdsalyer/LECTURES/Ecn200e/Kocherla.pdf.

The equity premium: A puzzle

2009-09-07T11:10:00.000-07:00

THE EQUITY PREMIUMA Puzzle*
Rajnish MEHRA
Columbia University, New York, NY 10027, USA
Edward C. PRESCOTTFederal Reserve Bank of MinneapolisUniversity of Minnesota, Minneapolis, MN 5545.5, USA.

Mehra, Rajnish; Edward C. Prescott (1985). "The Equity Premium: A Puzzle" (PDF). Journal of Monetary Economics 15: 145–161

A statistical perspective on ill-posed inverse problems

2009-09-03T12:14:00.000-07:00

A statistical perspective on ill-posed inverse problems
F O'Sullivan - Statistical Science, 1986 - jstor.org
Page 1. Statistical Science 1986, Vol. 1, No. 4, 502-527 A Statistical Perspectiveon Ill-posed Inverse Problems Finbarr O'Sullivan Abstract. ...

Matlab Symbolic Mathematics

2009-07-20T17:29:00.000-07:00

Matlab Symbolic Mathematics

'If you are using the Student Version of MATLAB, then you have access to the optional Symbolic Math Toolbox. If you are using a professional (non-student) version, then you must purchase this toolbox separately. If you do not know whether your version of MATLAB is equipped with the toolbox or not, try a few of the following exercises. If they work, you抳e got it. If not, you will have to skip over any exercise that asks you to perform computations with variables that have not been assigned numeric values and should be treated as symbols. '

See the above link for details.

The ET Interview: Professor Jan Kmenta

2009-07-09T13:22:00.000-07:00

The ET Interview: Professor Jan Kmenta
John Lodewijks and Jan Kmenta
Econometric Theory, Vol. 21, No. 3 (Jun., 2005), pp. 621-645
Published by: Cambridge University Press
Access article from an external site

Teaching Modeling and Simulation in Economics: A Pleasant Surprise

2009-07-09T11:29:00.000-07:00

Teaching Modeling and Simulation in Economics: A Pleasant Surprise
Eshragh Motahar
The Journal of Economic Education, Vol. 25, No. 4 (Autumn, 1994), pp. 335-342

Statistics on Statistics: Measuring Research Productivity by Journal Publications between 1985 and 1995

2009-07-09T11:26:00.001-07:00

Statistics on Statistics: Measuring Research Productivity by Journal Publications between 1985 and 1995
Christian Genest
The Canadian Journal of Statistics / La Revue Canadienne de Statistique, Vol. 25, No. 4 (Dec., 1997), pp. 427-443

A History of the Statistical Society of Canada: The Formative Years

2009-07-09T11:21:00.000-07:00

A History of the Statistical Society of Canada: The Formative Years
David R. Bellhouse, Christian Genest
Statistical Science, Vol. 14, No. 1 (Feb., 1999), pp. 80-115

The ET Dialogue: A Conversation on Econometric Methodology

2009-07-09T11:19:00.001-07:00

The ET Dialogue: A Conversation on Econometric Methodology
David F. Hendry, Edward E. Leamer, Dale J. Poirier
Econometric Theory, Vol. 6, No. 2 (Jun., 1990), pp. 171-261

Instrumental variable

2009-07-08T14:38:00.000-07:00

Instrumental Variable Estimation of the Simple Errors-in-Variables Model
R. L. Carter, Wayne A. Fuller
Journal of the American Statistical Association, Vol. 75, No. 371 (Sep., 1980), pp. 687-692

Instrumental-Variable Estimation of an Error-Components Model
Takeshi Amemiya, Thomas E. MaCurdy
Econometrica, Vol. 54, No. 4 (Jul., 1986), pp. 869-880

Instrumental Variable Estimation in Generalized Linear Measurement Error Models
Jeffrey S. Buzas, Leonard A. Stefanski
Journal of the American Statistical Association, Vol. 91, No. 435 (Sep., 1996), pp. 999-1006

Finite Sample Properties of Instrumental Variable Estimators of Structural Coefficients
Roberto S. Mariano
Econometrica, Vol. 45, No. 2 (Mar., 1977), pp. 487-496

Does More Crime Mean More Prisoners? An Instrumental Variables Approach
Yair Listokin
Journal of Law and Economics, Vol. 46, No. 1 (Apr., 2003), pp. 181-206

Testing Identifiability and Specification in Instrumental Variable Models
John G. Cragg, Stephen G. Donald
Econometric Theory, Vol. 9, No. 2 (Jun., 1993), pp. 222-240

Consistent Estimation with a Large Number of Weak Instruments
John C. Chao, Norman R. Swanson
Econometrica, Vol. 73, No. 5 (Sep., 2005), pp. 1673-1692

Structural Equations, Treatment Effects, and Econometric Policy Evaluation Structural Equations, Treatment Effects, and Econometric Policy Evaluation
James J. Heckman, Edward Vytlacil
Econometrica, Vol. 73, No. 3 (May, 2005), pp. 669-738

Calibration

2009-07-08T14:32:00.000-07:00

Introduction Calibration and Econometric Research: An Overview
Adrian Pagan
Journal of Applied Econometrics, Vol. 9, Supplement: Special Issue on Calibration Techniques and Eco... more
Published by: John Wiley & Sons

Statistical Computing with R

2009-07-05T17:27:00.000-07:00

Statistical Computing with RMaria L. Rizzo Chapman & Hall/CRC

Cat. #: C5459ISBN: 9781584885450
ISBN 10: 1584885459
Publication Date: 11/15/2007

Table of Contents and description.
R code for examples in the book (by chapter).R code for all examples in a single zip file: SCRcode.zip (revised 04/05/2008)
Errata and Notes (revised 11/26/2008).

DEA technical efficiency score

2009-07-05T15:32:00.000-07:00

function TE=techeff(X,Y)
%% techeff(X,Y) calculates the technical efficiency of decision making units%%% Input:% X: N x J matrix, with N inputs for each unit% Y: M x J matrix, with M outpus for each unit% J: # of decision making units%%% Output:% TE: J x 1 vetctor contains the technical efficiency of each DMU%%% Reference:% Hughes and Yaisawarng, 2004, "Sensitivity and dimensionality tests of DEA% efficiency scores," European Journal of Operational Research, 154,% p.410-422%%% Author information:% Yundong Tu% Department of Economics% University of California, Riverside% e-mail: yundong.tu@gmail.com% July 4, 2009
%check data inputs% if nargin<2% error(' Not enough input arguments to run techeff ')% end
if nargin<2 rand('twister',3); X=3.*rand(5,20); Y=5.*rand(3,20);end
%check dimension compatibilityif size(X,2)~=size(Y,2) error(' Input data are not compatible. Inputs and outputs must have the same collumns, i.e., for the same number of DMUs')end
options=optimset('Display','off');%,'MaxIter',100,'MaxFunEvals',100,'TolX',1e-2,'TolFun',1e-2);for k=1:size(X,2) [z,TE(k,1)]=linprog([zeros(size(X,2),1);1.0], [-Y,zeros(size(Y,1),1);X, -X(:,k)], [-Y(:,k);zeros(size(X,1),1.0)],... [ones(1,size(X,2)),0.0], 1.0,zeros(size(X,2)+1,1),ones(size(X,2)+1,1), 0.5.*ones(size(X,2)+1,1),options);end

Calling R from within Matlab

2009-07-05T12:07:00.000-07:00

The COM interface allows Matlab users to call R from within Matlab. It is quite convenient for matlab users to interact with R functions. To make R project available to your matlab is very simple.

TO DO LIST:
1. Install Matlab: http://www.mathworks.com/
2. Install R: Open http://www.r-project.org/ , choose download R and then select a mirror.
3. Install the R package "rscproxy" in R. The package is available at: http://cran.r-project.org/. Go to package and find rscproxy. This can also be simply done by typing "install.packages('rscproxy') in R prompt. Then choose a mirror. Wait for 2 seconds and it is done.
4. Download R-(D)COM Interface by clicking R_Scilab_DCOM3.0-1B5.exe .
5. Download MATLAB R-link from: http://www.mathworks.com/matlabcentral/fileexchange/5051
6. Unzip the downloaded MATLAB R-link.zip into your current directory in matlab.
7. You can enjoy the convenience of having Matlab to call R now. Test if it is working by type "Rdemo" in Matlab commond window. If you are interested in nonparametric denstiy estimation, run the following MatlabcallRnp.m file

function MatlabcallRnp()
%% MatlabcallRnp() illustrates how to use Matlab to call the %% NP package in R. %% Note: all .m files in the Matlab_RLINK folder should be %% copied into the current directory in Matlab. You do not %% need run R when it is called.% Author Infor.% Yundong Tu% Department of Economics,% Univeristy of California, Riverside% e-mail: yundong.tu@email.ucr.edu
%% Connect to an R SessionopenR
%% Push data into R with putRdata()a = randn(200,1);putRdata('a',a)%%{%% Call the density (R function to estimate density) %% command into Matlab with evalR() %get the evaluation points for the density estimator xx= evalR('density(a)$x'); %get the corresponding evaluation of density fx= evalR('density(a)$y'); %figure subplot(2,1,1) plot(xx,fx); %plot the density function% %the density plot can be also called by R as evalR('plot(density(a),mfrow=c(2,1))');%}
%% Call the npudens (R function to estimate density) %% command into Matlab with evalR() %get the evaluation points for the density estimator evalR('data=data.frame(a)'); evalR('library(np)')
evalR('xx=npudens(data)$eval'); %dataframe xx=evalR('xx[[1]]') %matrix %get the corresponding evaluation of density fx= evalR('npudens(data)$dens') %figure %xy=eda; [xx,ind]=sort(xx); fx=fx(ind); subplot(2,1,2) plot(xx,fx); %plot the density function %the npudens plot can be also called by R as evalR('plot(npudens(a),add=FALSE)');%}%%{%% Run a series of commands and grab %% the result using getRdata()%save time to call density() just once, also get the bandwidthevalR('den=density(a)'); xx=evalR('den$x'); % the same as: evalR('xx=den$x'); xx=getRdata('xx');fx=evalR('den$y'); bw=evalR('den$bw');
figureplot(xx,fx);hold ontitle({['R-output DENSITY'];['Bandwidth=',num2str(bw)]});hold off%}%% Close the connectioncloseR

Other related links:
http://www.cs.ubc.ca/~murphyk/Software/callingRfromMatlab.html
http://webscripts.softpedia.com/script/Scientific-Engineering-Ruby/Statistics-and-Probability/MATLAB-R-link-35485.html

http://neurochannels.blogspot.com/2010/05/how-to-run-r-code-in-matlab.html

The Pride of Econometrician

Senior Project Archive

Graphics inclusion

supported file types

epstopf: including eps-graphics in a pdfLaTeX-document

Add (Hyper-)Links to PDFs

Add (Hyper-)Links to PDFs

WinEdt 6: font changing

WinEdt 6: font changing

All Models Are Wrong But Some Are Useful

Generalized Information Measures and Their Applications

Book: Forecasting with Exponential Smoothing The State Space Approach

Forecasting with Exponential SmoothingThe State Space Approach,Rob Hyndman, Anne Koehler, Keith Ord and Ralph SnyderSpringer Link

Information Theoretic Research

Information Theory Research Group

Type I or Type II error?

An interesting discussion with how to memorize these two concepts.

Type I and Type II Errors

Fuzzy Least Square Estimation

Maximum Rank Correlation Estimators

Cosma Rohilla Shalizi

The Epic Story of Maximum Likelihood

Institute of Mathematical Statistics Lecture Notes - Monograph Series

A LaTeX link from MIT

Matrix Decomposition

The analysis of contingency tables under inequality constraints

Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space

Nonlinear Hypotheses, Inequality Restrictions, and Non-Nested Hypotheses

The Sucess of Econometrics

In Memory of John Denis Sargan

Finite Sample Properties of Bootstrap GMM

The Bootstrap’s Finite Sample Distribution

FINITE SAMPLE APPROXIMATION RESULTS FOR PRINCIPAL COMPONENT ANALYSIS

Thomas S. Ferguson: BIOGRAPHY

A Course in Large Sample Theory

Asymptotic Theory in Probability and Statistics with Applications

Common Features in Economics and Finance

Resampling methods in econometrics

Thirty-five years of journal of econometrics

Inverse Problems in Econometrics

NONPARAMETRIC CURVE ESTIMATION: AN OVERVIEW

Matrix Algebra in R: Resources, Videos, Textbooks

A Brief History of Linear Algebra and Matrix Theory

Mathematical methods for economic theory

Engeneering Statistics Handbook

R: Probit Model

Music Gallery

A New Era: A Beautiful Mind

R: Linear Regression Example of Faraway (2002)

R: replacing for loop by apply

A plot example

tapply for aggregate statistics

Subsetting data frame in R

Text Processing using LaTeX

R: snow Simplified

Matlab is Great; R is Exciting!

Degrees of Freedom

Prior information

Mankiw on Bernanke

Gelman on Efron: Bayesian statistics

Monetary Policy and Asset Bubbles in 2010

Video: Challenging Bernanke on Housing Bust

Lars Hansen: Macroeconomic Risk

An Interview with Lars Hansen

World Economy 2010: Better or Worse?

Lousy Investment in Housing Market?

Personal Credit Crisis of An Economist

Complexity of Macroeconomics

A blog on Latex and related issues

A Beamer Quickstart

Residue Theorem and Its Application

STATISTICS: REFLECTIONS ON THE PAST AND VISIONS FOR THE FUTURE

Multivariate t-distribution

Central Limit Theorem

Law of Large Numbers

Bootstrap: Collection in Statistical Sicence (2003)

On readings R. A. Fisher

Boosting

Bayesian Econometrics Methods

Markov Chain Monte Carlo (1)

Forecasting with Exponential Smoothing
The State Space Approach,Rob Hyndman, Anne Koehler, Keith Ord and Ralph SnyderSpringer Link