The Annals of Statistics

Regression M-estimators with non-i.i.d. doubly censored data

Jian-Jian Ren

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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.

Article information

Ann. Statist., Volume 31, Number 4 (2003), 1186-1219.

First available in Project Euclid: 31 July 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J05: Linear regression 62N02: Estimation 62E20: Asymptotic distribution theory

Asymptotic normality generalized weighted empirical process Hadamard differentiability linear regression model strong consistency weak convergence


Ren, Jian-Jian. Regression M -estimators with non-i.i.d. doubly censored data. Ann. Statist. 31 (2003), no. 4, 1186--1219. doi:10.1214/aos/1059655911.

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