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

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.