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August 2003 Regression M-estimators with non-i.i.d. doubly censored data
Jian-Jian Ren
Ann. Statist. 31(4): 1186-1219 (August 2003). DOI: 10.1214/aos/1059655911


Considering the linear regression model with fixed design, the usual M-estimator} with a complete sample of the response variables is expressed as a functional of a generalized weighted bivariate empirical process, and its asymptotic normality is directly derived through the Hadamard differentiability property of this functional and the weak convergence of this generalized weighted empirical process. The result reveals the direct relationship between the M-estimator and the distribution function of the error variables in the linear model, which leads to the construction of the M-estimator} when the response variables are subject to double censoring. For this proposed regression M-estimator with non-i.i.d. doubly censored data, strong consistency and asymptotic normality are established.


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Jian-Jian Ren. "Regression M-estimators with non-i.i.d. doubly censored data." Ann. Statist. 31 (4) 1186 - 1219, August 2003.


Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1041.62055
MathSciNet: MR2001648
Digital Object Identifier: 10.1214/aos/1059655911

Primary: 62E20 , 62J05 , 62N02

Keywords: asymptotic normality , generalized weighted empirical process , Hadamard differentiability , linear regression model , strong consistency , weak convergence

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • August 2003
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