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.
Publié le : 1997-12-14
Classification:
Asymptotic normality,
bivarate distribution function,
bivariate right-censored data,
consistency,
Hadamard differentiability,
linear regression model,
$M$-estimators,
statistical functional,
weak convergence,
62G05,
62J05,
62E20
@article{1030741089,
author = {Ren, Jian-Jian and Gu, Minggao},
title = {Regression M-estimators with doubly censored data},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 2638-2664},
language = {en},
url = {http://dml.mathdoc.fr/item/1030741089}
}
Ren, Jian-Jian; Gu, Minggao. Regression M-estimators with doubly censored data. Ann. Statist., Tome 25 (1997) no. 6, pp. 2638-2664. http://gdmltest.u-ga.fr/item/1030741089/