Type I or Type II error?

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

Institute of Mathematical Statistics Lecture Notes - Monograph Series

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

A Course in Large Sample Theory

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

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.

Engeneering Statistics Handbook

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

Degrees of Freedom

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

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.

Gelman on Efron: Bayesian statistics

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

STATISTICS: REFLECTIONS ON THE PAST AND VISIONS FOR THE FUTURE

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)

Springer Texts in Statistics

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

Glance at Advanced Statistics: Linear Regression

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

40 Puzzles and Problems in Probability and Mathematical Statistics

SpringerLink Book series
Problem Books in Mathematics

Digest of Education Statistics

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