The Annals of Statistics

Large Sample Theory of a Modified Buckley-James Estimator for Regression Analysis with Censored Data

Tze Leung Lai and Zhiliang Ying

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Abstract

Buckley and James proposed an extension of the classical least squares estimator to the censored regression model. It has been found in some empirical and Monte Carlo studies that their approach provides satisfactory results and seems to be superior to other extensions of the least squares estimator in the literature. To develop a complete asymptotic theory for this approach, we introduce herein a slight modification of the Buckley-James estimator to get around the difficulties caused by the instability at the upper tail of the associated Kaplan-Meier estimate of the underlying error distribution and show that the modified Buckley-James estimator is consistent and asymptotically normal under certain regularity conditions. A simple formula for the asymptotic variance of the modified Buckley-James estimator is also derived and is used to study the asymptotic efficiency of the estimator. Extensions of these results to the multiple regression model are also given.

Article information

Source
Ann. Statist., Volume 19, Number 3 (1991), 1370-1402.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348253

Digital Object Identifier
doi:10.1214/aos/1176348253

Mathematical Reviews number (MathSciNet)
MR1126329

Zentralblatt MATH identifier
0742.62043

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation 60F05: Central limit and other weak theorems

Keywords
Linear regression censoring least squares estimator empirical process martingale

Citation

Lai, Tze Leung; Ying, Zhiliang. Large Sample Theory of a Modified Buckley-James Estimator for Regression Analysis with Censored Data. Ann. Statist. 19 (1991), no. 3, 1370--1402. doi:10.1214/aos/1176348253. https://projecteuclid.org/euclid.aos/1176348253


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