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Re: st: Normally distributed error term & testing normality of residuals


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Normally distributed error term & testing normality of residuals
Date   Sun, 14 Oct 2012 10:32:09 -0400

On Sat, Oct 13, 2012 at 7:09 PM, Justina Fischer <JAVFischer@gmx.de> wrote:
> A formal test of normality would be the Jarque-Bera-test of normality, available as user written programme called -jb6-.
> It gives nice test stats that can be reported in a paper.
> (is there s.th. newer available?)
>
> I prefer using the Jarque-Bera combined with -qnorm- (see below, which allows to label the single obs) in order to identify outlier observations.

The way that residuals are created can make them look more normal than
the underlying errors simply due to being linear combinations of the y
and thus subject to extra smoothing due to the Central Limit Theorem.
Thus if y has non-normal errors, the corresponding residuals will be a
function of multiple errors and thus are likely to appear more normal.
For instance, if the errors are exponential the residuals will involve
weighted averages of exponentials, which will start to look
chi-square.

Regardless, residuals from a Tobit regression will not be normal due
to the censoring, and there's no straightforward way to fix that up
given that you don't observe what happens for censored cases.
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