Advances and Applications in Statistics
Volume 53, Issue 2, Pages 153 - 164
(August 2018) http://dx.doi.org/10.17654/AS053020153 |
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LINEAR REGRESSION WITH NON-NORMAL ERRORS
Na Li and Jan Vrbik
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Abstract: We explain how to find an accurate approximation of the sampling distribution of ML estimators relating to simple linear regression with non-normal errors. Using Edgeworth series, our method achieves a substantially better accuracy than the usual normal approximation, based on Fisher information matrix. This is demonstrated by using examples of logistic, Cauchy and Gumbel distributions for the regression’s error terms. |
Keywords and phrases: linear regression, non-normal errors, MLE, asymptotic distribution, Edgeworth expansion. |
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