Estimation of central shapes of error distributions in linear regression problems
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 <Subscript> p </Subscript> 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
Year of publication: |
2013
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Authors: | Lai, P. ; Lee, Stephen |
Published in: |
Annals of the Institute of Statistical Mathematics. - Springer. - Vol. 65.2013, 1, p. 105-124
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Publisher: |
Springer |
Saved in:
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