The Annals of Statistics

Asymptotic Properties of Censored Linear Rank Tests

Jack Cuzick

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Abstract

A conjecture of Prentice is established which states that for censored linear rank test, exact scores based on conditional expectations can be replaced by approximate scores obtained by evaluating the score function at an estimate of the survival function. We show that under minimal conditions, asymptotically equivalent tests are obtained when either the Kaplan-Meier, Altshuler, or moment estimator of the survival function is used. Asymptotic normality is also established for a general random censorship model under the null hypothesis, and for contiguous alternatives. This is used to calculate efficacies, and when the censoring times are i.i.d., an expression for the asymptotic relative efficiency is given which is a natural generalization of the one for classical uncensored linear rank tests.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 133-141.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346581

Digital Object Identifier
doi:10.1214/aos/1176346581

Mathematical Reviews number (MathSciNet)
MR773157

Zentralblatt MATH identifier
0584.62069

JSTOR
links.jstor.org

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62P10: Applications to biology and medical sciences 60F05: Central limit and other weak theorems 62N05: Reliability and life testing [See also 90B25]

Keywords
Linear rank test censored data approximate scores central limit theorem asymptotic relative efficiency

Citation

Cuzick, Jack. Asymptotic Properties of Censored Linear Rank Tests. Ann. Statist. 13 (1985), no. 1, 133--141. doi:10.1214/aos/1176346581. https://projecteuclid.org/euclid.aos/1176346581


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