The Annals of Statistics

A Large Sample Study of Rank Estimation for Censored Regression Data

Zhiliang Ying

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Abstract

Large sample approximations are developed to establish asymptotic linearity of the commonly used linear rank estimating functions, defined as stochastic integrals of counting processes over the whole line, for censored regression data. These approximations lead to asymptotic normality of the resulting rank estimators defined as solutions of the linear rank estimating equations. A second kind of approximations is also developed to show that the estimating functions can be uniformly approximated by certain more manageable nonrandom functions, resulting in a simple condition that guarantees consistency of the rank estimators. This condition is verified for the two-sample problem, thereby extending earlier results by Louis and Wei and Gail, as well as in the case when the underlying error distribution has increasing failure rate, which includes most parametric regression models in survival analysis. Techniques to handle the delicate tail fluctuations are provided and discussed in detail.

Article information

Source
Ann. Statist., Volume 21, Number 1 (1993), 76-99.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349016

Digital Object Identifier
doi:10.1214/aos/1176349016

Mathematical Reviews number (MathSciNet)
MR1212167

Zentralblatt MATH identifier
0773.62048

JSTOR
links.jstor.org

Subjects
Primary: 62J05: Linear regression
Secondary: 60F05: Central limit and other weak theorems 62F12: Asymptotic properties of estimators 62G05: Estimation

Keywords
Accelerated life model censored regression log-rank statistic asymptotic linearity consistency asymptotic normality counting process

Citation

Ying, Zhiliang. A Large Sample Study of Rank Estimation for Censored Regression Data. Ann. Statist. 21 (1993), no. 1, 76--99. doi:10.1214/aos/1176349016. https://projecteuclid.org/euclid.aos/1176349016


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