Open Access
Translator Disclaimer
December 1997 Regression M-estimators with doubly censored data
Jian-Jian Ren, Minggao Gu
Ann. Statist. 25(6): 2638-2664 (December 1997). DOI: 10.1214/aos/1030741089


The M-estimators are proposed for the linear regression model with random design when the response observations are doubly censored. The proposed estimators are constructed as some functional of a Campbell-type estimator $\hat{F}_n$ for a bivariate distribution function based on data which are doubly censored in one coordinate. We establish strong uniform consistency and asymptotic normality of $\hat{F}_n$ and derive the asymptotic normality of the proposed regression M-estimators through verifying their Hadamard differentiability property. As corollaries, we show that our results on the proposed M-estimators also apply to other types of data such as uncensored observations, bivariate observations under univariate right censoring, bivariate right-censored observations, and so on. Computation of the proposed regression M-estimators is discussed and the method is applied to a doubly censored data set, which was encountered in a recent study on the age-dependent growth rate of primary breast cancer.


Download Citation

Jian-Jian Ren. Minggao Gu. "Regression M-estimators with doubly censored data." Ann. Statist. 25 (6) 2638 - 2664, December 1997.


Published: December 1997
First available in Project Euclid: 30 August 2002

zbMATH: 0907.62045
MathSciNet: MR1604432
Digital Object Identifier: 10.1214/aos/1030741089

Primary: 62G05 , 62J05
Secondary: 62E20

Keywords: $M$-estimators , asymptotic normality , bivarate distribution function , bivariate right-censored data , consistency , Hadamard differentiability , linear regression model , statistical functional , weak convergence

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 6 • December 1997
Back to Top