The Bahadur-Kiefer Representation of Lp Regression Estimators

Miguel A. Arcones

Econometric Theory, 1996, vol. 12, issue 2, 257-283

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 thatHere, 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.

Date: 1996
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