Open Access
April, 1995 An Omnibus Test for Independence of a Survival Time from a Covariate
Ian W. McKeague, A. M. Nikabadze, Yanqing Sun
Ann. Statist. 23(2): 450-475 (April, 1995). DOI: 10.1214/aos/1176324530


It has been over 60 years since Kolmogorov introduced a distribution-free omnibus test for the simple null hypothesis that a distribution function coincides with a given distribution function. Doob subsequently observed that Kolmogorov's approach could be simplified by transforming the empirical process to an empirical process based on uniform random variables. Recent use of more sophisticated transformations has led to the construction of asymptotically distribution-free omnibus tests when unknown parameters are present. The purpose of the present paper is to use the transformation approach to construct an asymptotically distribution-free omnibus test for independence of a survival time from a covariate. The test statistic is obtained from a certain test statistic process (indexed by time and covariate), which is shown to converge in distribution to a Brownian sheet. A simulation study is carried out to investigate the finite sample properties of the proposed test and an application to data from the British Medical Research Council's 4th myelomatosis trial is given.


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Ian W. McKeague. A. M. Nikabadze. Yanqing Sun. "An Omnibus Test for Independence of a Survival Time from a Covariate." Ann. Statist. 23 (2) 450 - 475, April, 1995.


Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0829.62054
MathSciNet: MR1332576
Digital Object Identifier: 10.1214/aos/1176324530

Primary: 62G10
Secondary: 62G20

Keywords: counting processes , distribution-free , Goodness-of-fit , innovation Brownian sheet , martingale methods

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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