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M-estimation in linear models under nonstandard conditions

✍ Scribed by Faouzi El Bantli

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
291 KB
Volume
121
Category
Article
ISSN
0378-3758

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✦ Synopsis

The limiting distribution of M-estimators of the regression parameter in linear models is derived under nonstandard conditions, allowing, e.g., for discontinuities in density functions. Unlike usual regularity assumptions, our conditions are satisΓΏed, for instance, in the case of regression quantiles, hence also in the context of L1 estimation; our results thus extend those of Knight (Ann. Statist. 26 (1998) 755). The resulting asymptotic distributions, in general, are not Gaussian. Therefore, the limiting bootstrap distributions of these estimators are also investigated. It is shown that bootstrap approximations are correct to the ΓΏrst order only when limiting distributions are Gaussian, or along speciΓΏc sequences mn of bootstrap sample sizes. Numerical examples are given to illustrate these asymptotic results.

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