The Annals of Probability

Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications

Paul Deheuvels and John H. J. Einmahl

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Abstract

We prove functional limit laws for the increment functions of empirical processes based upon randomly right-censored data. The increment sizes we consider are classified into different classes covering the whole possible spectrum. We apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions. In particular, we treat the case of kernel density and hazard rate estimators.

Article information

Source
Ann. Probab., Volume 28, Number 3 (2000), 1301-1335.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160336

Digital Object Identifier
doi:10.1214/aop/1019160336

Mathematical Reviews number (MathSciNet)
MR1797314

Zentralblatt MATH identifier
1016.62031

Subjects
Primary: 62G05: Estimation 60F15: Strong theorems 60F17: Functional limit theorems; invariance principles
Secondary: 62E20: Asymptotic distribution theory 62P10: Applications to biology and medical sciences

Keywords
Density and hazard rate estimation functional law of the iterated logarithm random censorship strong limit theorems

Citation

Deheuvels, Paul; Einmahl, John H. J. Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications. Ann. Probab. 28 (2000), no. 3, 1301--1335. doi:10.1214/aop/1019160336. https://projecteuclid.org/euclid.aop/1019160336


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