The Annals of Statistics

Estimation in a Linear Regression Model with Censored Data

Y. Ritov

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 18, Number 1 (1990), 303-328.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347502

Digital Object Identifier
doi:10.1214/aos/1176347502

Mathematical Reviews number (MathSciNet)
MR1041395

Zentralblatt MATH identifier
0713.62045

JSTOR
links.jstor.org

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G05: Estimation

Keywords
Buckley-James estimator counting process Kaplan-Meier estimator martingales

Citation

Ritov, Y. Estimation in a Linear Regression Model with Censored Data. Ann. Statist. 18 (1990), no. 1, 303--328. doi:10.1214/aos/1176347502. http://projecteuclid.org/euclid.aos/1176347502.


Export citation