15 Error Non-Gaussian Distribution

15 Error Non-Gaussian Distribution - Economics 140A Error:...

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Unformatted text preview: Economics 140A Error: Non-Gaussian Distribution We come to the &nal assumption, which states that the regression model error has a Gaussian distribution. How are the properties of our estimators a/ected? Dramatically. The &nite sample distribution of the OLS estimator arises from the fact that a &nite sum of Gaussian random variables has a Gaussian distribution. Such a result does not hold for general distributions. As a result, the &nite sample distribution of the estimator is typically unknown if the error is not Gaussian. (The asymptotic distribution of the estimator is still easily obtained.) Perhaps the most common departure from a Gaussian assumption is the as- sumption that the errors have a t-distribution. As you recall, the t-distribution allows for more outliers (and more inliers) than does a Gaussian distribution. The t-distribution with & degrees-of-freedom is f W ( w ) = & & & +1 2 ¡ & & 1 2 ¡ & & & 2 ¡ ¢ 1 + w 2 ¡ £ & ( & +1) 2 ¡ 1 2 ; where & ( & ) is the gamma function. (Aside: The gamma function is de&ned for s > as & ( s ) ¡ Z 1 x s & 1 e & x dx: The gamma function has a simple algebraic form only for special cases, one of...
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This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.

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15 Error Non-Gaussian Distribution - Economics 140A Error:...

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