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June, 1986 Empirical Processes Associated with $V$-Statistics and a Class of Estimators Under Random Censoring
Michael G. Akritas
Ann. Statist. 14(2): 619-637 (June, 1986). DOI: 10.1214/aos/1176349942


A class of empirical processes associated with $V$-statistics ($V$-empirical process) under random censoring, and a class of nonparametric estimators based on the corresponding quantile process are defined. The $V$-empirical process is the censored data analogue of the $U$-empirical process considered by Silverman (1976, 1983). The class of estimators is the analogue of the class of generalized $L$-statistics introduced by Serfling (1984) and it includes the results of Sander (1975). The weak convergence of the $V$-empirical process and the corresponding quantile process is obtained and, through that, the asymptotic behavior of the estimators is studied. Linear bounds for the Kaplan-Meier estimator near the origin are established. A number of examples are given, including the generalization of the Hodges-Lehmann estimator for estimating the treatment effect in the two-sample problem under random censoring. A measure of spread, a procedure for estimation in the two-way ANOVA model, and a modified version of the two-sample Hodges-Lehmann estimator, all of which are new even in the uncensored case, are proposed.


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Michael G. Akritas. "Empirical Processes Associated with $V$-Statistics and a Class of Estimators Under Random Censoring." Ann. Statist. 14 (2) 619 - 637, June, 1986.


Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0603.62046
MathSciNet: MR840518
Digital Object Identifier: 10.1214/aos/1176349942

Primary: 62G05
Secondary: 62E20, 62G30

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 2 • June, 1986
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