The Bahadur-Kiefer Representation ofLpRegression Estimators

Author:

Arcones Miguel A.

Abstract

We consider the following linear regression model:whereare independent and identically distributed random variables, Yi, is real, Zihas values in Rm, Ui, is independent of Zi, and θ0is anm-dimensional parameter to be estimated. TheLpestimator of θ0is 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,whereandcis a positive constant, which depends onpand on the random variableX.

Publisher

Cambridge University Press (CUP)

Subject

Economics and Econometrics,Social Sciences (miscellaneous)

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