The Annals of Statistics

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

Jian-Jian Ren

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 31 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1059655911

Digital Object Identifier
doi:10.1214/aos/1059655911

Mathematical Reviews number (MathSciNet)
MR2001648

Zentralblatt MATH identifier
1041.62055

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1059655911


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  • ORLANDO, FLORIDA 32816 E-MAIL: jren@mail.ucf.edu