Estimation in a Linear Regression Model with Censored Data

Abstract

We consider the semiparametric linear regression model with censored data and with unknown error distribution. We describe estimation equations of the Buckley-James type that admit $\sqrt n$-consistent and asymptotically normal solutions. The derived estimator is efficient at a particular error distribution. We show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by Tsiatis. This equivalence is an extension of a basic equivalence between Doob type martingales and counting process martingales shown by Ritov and Wellner. An extension to an estimator that is efficient everywhere is discussed.