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The Bahadur-Kiefer Representation of Lp Regression Estimators

Published online by Cambridge University Press:  11 February 2009

Miguel A. Arcones
Miguel A. Arcones
Affiliation:
University of Texas, Austin
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Abstract

We consider the following linear regression model:

where are independent and identically distributed random variables, Yi, is real, Zi has values in Rm, Ui, is independent of Zi, and θ0 is an m-dimensional parameter to be estimated. The Lp estimator of θ0 is the value 6n such that

Here, we will give the exact Bahadur-Kiefer representation of θn, for each p ≥ 1. Explicitly, we will see that, under regularity conditions,

where and c is a positive constant, which depends on p and on the random variable X.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 2 , June 1996 , pp. 257 - 283
Copyright
Copyright © Cambridge University Press 1996

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References

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