Koul-DeWet-type estimation in censored regression using the conditional empirical process

Abstract

Assume that the random variables of interest obey a linear regression model and are randomly censored by independent censoring variables. We consider some minimum distance estimators of the slope parameter. These estimators are asymptotically normal at the assumed regression model and are also qualitatively robust against small Kolmogorov distance deviation from the model. They are adapted from the Koul-DeWet ( Ann. Statist. 11 (1983), 921–932) estimators via a conditioning argument. As a result the conditions on the censoring distributions are very mild.