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.
@article{1176347502,
author = {Ritov, Y.},
title = {Estimation in a Linear Regression Model with Censored Data},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 303-328},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347502}
}
Ritov, Y. Estimation in a Linear Regression Model with Censored Data. Ann. Statist., Tome 18 (1990) no. 1, pp. 303-328. http://gdmltest.u-ga.fr/item/1176347502/