9:59 PM Amy: about Prof. Ullah's paper last Friday, what's the main point? Have he and Yongbao developed some estimation even when the error term is nonnormal?
Yundong Tu to Amy show details 10:18 PM (19 hours ago) Reply
Their papers are not to develope estimation result but to provide finite sample approximation for higher order moments of the estimators ( estimators, say beta hat, are taken as given, which can be MLE, GMM, IV, LS, etc.). The other paper is about expectation of quadradict form. They also provide finite sample approximation for these terms. Finite sample approximation differs when the error terms are nonnormally distributed from normally distributed case. These approximation results, however, could be used to study the properties of some other estimators, for example, the estimator of rho in the spatial autoregressive model, or the estimators of the coefficients in the MA or AR models.
10:29 PM Amy: so when error tems are nonnormal, we can still estimate the coefficients such as in VAR models. What 's the difference between this way and other methods approximating nonnormal errors to a normal distribution?
10:31 PM me: yes, you still can estimate using the same method as if the error term is normal
Amy: in Ullah's way?
me: no the classical way he is sillent about the estimation approach he is only concerned with the moments of the estimators
10:32 PM which is not quite a concern in macro, i think
Amy: but you say we can still estimate the coefficients me: yes
Amy: That's what I am considering
me: but we do not know the higher oder moments the properties of that is provided by Ullah and Bao
10:33 PM Amy: when the error term is nonnormal, could we use some methods of finite sample to estimate> Since they mention the MLE
me: finite sample is not to estimate the coefficients but to approximate higher order moments, say skewness and kurtosis of the estimators
10:34 PM Amy: I see. I am not familiar with finte sample
me: yes, you can still use MLE, GMM, IV and LS, etc. for the estimation purpose but once you get these estimators, you might be interested in its higher order properties the estimator you get would be not normally distributed
10:35 PM especially when the error term is not normally distributed and when the sample is small or even moderate large not even close to normal
Amy: I c.
me: finite sample approach is one method to tell how far is your estimator from a normal random variable
10:36 PM typical way to examine this is to check the property of skewness and kurtosis and see how far they are from those of normal distribution
10:37 PM in large sample, everything (estimator) is normally distributed, so there is no difference but what we have usually is not large sample observations
10:38 PM this leaves a room for finite sample theory to improve upon the large sample theory to get more accurate properties of the estimators we derived
Amy: But what will we do if we find the estimator is not normal distribution?
10:39 PM me: we impose finite sample corrections then
10:41 PM you know that for normally distributed random variable, skewness is zero and kurtosis is 3. if it is not normally distributed Ullah and Bao provide formula for those, which should also be used when sample size is small
10:42 PM Amy: I know that. But how to corret them?
10:43 PM me: use the fomula in Ullah and Bao for Skewness and Kurtosis
Amy: and then?
me: In Ullah's book, there should be fomula for mean and variance
10:45 PM Amy: I see. Maybe I should read the book firstly. But is there any way to use this correction way for estimation?
me: no it is not for estimation of the coefficient in econometric models like y=xb+e
10:46 PM their method is silent about the estimation approach, as i said earlier it can be used for a general class of estimators called extremum estimators
10:47 PM Amy: I c. Thank you. me: their approximation result depends on the following assumption sqrt(n)(bhat-b) converges to a normal distribution it's a pleasure
10:48 PM Amy: see. Thanks a million~~ I am looking at your pics in picasa
10:49 PM me: :)
10:51 PM Amy: ok, night~~ good dream.
me: u2
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