Advances and Applications in Statistics
Volume 54, Issue 2, Pages 237 - 253
(February 2019) http://dx.doi.org/10.17654/AS054020237 |
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LINEAR REGRESSION WITH MIS-SPECIFIED ERROR DISTRIBUTION
Na Li, Jan Vrbik and Xiaojian Xu
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Abstract: We make two modifications to the simple regression model: first we obtain an analytical form of asymptotic sampling distributions of maximum likelihood (ML) estimators by linearizing and solving the normal equations when the error distribution is non-normal but symmetric (such as Cauchy, logistic or Laplace); we also include one asymmetric example (Gumbel). This approach then enables us to deal with situations when the error distribution is mis-specified, resulting in a loss of efficiency in the β1 estimation, and distortion of the corresponding confidence interval. |
Keywords and phrases: robustness, Fisher information, efficiency, asymptotic sampling distributions, confidence intervals.
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