Estimation in a Linear Regression Model with Censored Data
Open Access
- 1 March 1990
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 18 (1) , 303-328
- https://doi.org/10.1214/aos/1176347502
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.Keywords
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