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Efficiency and Robustness of a Resampling M-Estimator in the Linear Model

✍ Scribed by Feifang Hu

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
156 KB
Volume
78
Category
Article
ISSN
0047-259X

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✦ Synopsis

In the literature, there are basically two kinds of resampling methods for least squares estimation in linear models; the E-type (the efficient ones like the classical bootstrap), which is more efficient when error variables are homogeneous, and the R-type (the robust ones like the jackknife), which is more robust for heterogeneous errors. However, for M-estimation of a linear model, we find a counterexample showing that a usually E-type method is less efficient than an R-type method when error variables are homogeneous. In this paper, we give sufficient conditions under which the classification of the two types of the resampling methods is still true.

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The traditional method for estimating the linear function of fiied parameters in mixed linear model is a two-stage p r d u r e . In the first stage of this procedure the variance components estimators are calculated and next in the second stage these estimators are taken as true values of variance c