On Sun, 21 Jul 2002, David Greenberg wrote:
> Inferential statistics in OLS regression depend on the assumption that
> the distribution of residuals - that is to say, the distribution of
> scores on the dependent variable, conditional on the values of the
> predictors - is normal. The Central Limit Theorem is not relevant. It
> guarantees that parameter estimates will be normally distributed under
> certain circumstances. Those circumstances include the residuals being
> normally distributed.
The CLT is relevant in OLS and many other models because, as
another poster noted, a great many estimators are simply
complicated means. Only the exact small sample properties of
OLS are dependent on the normality of the errors (not the
residuals). For samples of reasonable size, inference in OLS
is not dependent on the assumption that the errors are normal.
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