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June, 1984 Asymptotic Behavior of Two-Sample Rank Tests in the Presence of Random Censoring
Sue Leurgans
Ann. Statist. 12(2): 572-589 (June, 1984). DOI: 10.1214/aos/1176346506


Two samples, $\{X_{ji}, 1 \leq i \leq n(j)\} (j = 1, 2)$ are assumed to be composed of iid random variables with survival functions $(1 - F_j)(1 - H_j)$, where $H$ is the cdf of the "censoring times" and $F$ is the cdf of the "true lifetimes." A unified derivation of the Pitman efficiencies of a class of rank statistics for censored samples is presented. The conditions under which the result holds do not require contiguous alternatives, since convergence to normality is shown to hold uniformly in equicontinuous $(F_1, F_2, H_1, H_2)$ with bounded hazard rates. The uniformity is obtained by studying a convenient joint representation of several counting processes. The results are applied to the translated exponential distributions, a noncontiguous family of alternatives.


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Sue Leurgans. "Asymptotic Behavior of Two-Sample Rank Tests in the Presence of Random Censoring." Ann. Statist. 12 (2) 572 - 589, June, 1984.


Published: June, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0544.62048
MathSciNet: MR740912
Digital Object Identifier: 10.1214/aos/1176346506

Primary: 62G20
Secondary: 62E20

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 2 • June, 1984
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