Estimation of central shapes of error distributions in linear regression problems

P. Lai () and Stephen Lee ()

Annals of the Institute of Statistical Mathematics, 2013, vol. 65, issue 1, 105-124

Abstract: Consider a linear regression model subject to an error distribution which is symmetric about 0 and varies regularly at 0 with exponent ζ. We propose two estimators of ζ, which characterizes the central shape of the error distribution. Both methods are motivated by the well-known Hill estimator, which has been extensively studied in the related problem of estimating tail indices, but substitute reciprocals of small L p residuals for the extreme order statistics in its original definition. The first method requires careful choices of p and the number k of smallest residuals employed for calculating the estimator. The second method is based on subsampling and works under less restrictive conditions on p and k. Both estimators are shown to be consistent for ζ and asymptotically normal. A simulation study is conducted to compare our proposed procedures with alternative estimates of ζ constructed using resampling methods designed for convergence rate estimation. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Keywords: Centre exponent; L p estimator; Regression; Subsampling (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10463-012-0360-2

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