The Annals of Probability

On the strong limiting behavior of local functionals of empirical processes based upon censored data

Paul Deheuvels and John H. J. Einmahl

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Abstract

We prove functional laws of the iterated logarithm for empirical processes based upon censored data in the neighborhood of a fixed point. We apply these results to obtain strong laws for estimators of local functionals of the lifetime distribution. In particular, we describe the pointwise strong limiting behavior of the kernel density estimator based upon the Kaplan-Meier product-limit estimator.

Article information

Source
Ann. Probab., Volume 24, Number 1 (1996), 504-525.

Dates
First available in Project Euclid: 15 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1042644729

Digital Object Identifier
doi:10.1214/aop/1042644729

Mathematical Reviews number (MathSciNet)
MR1387648

Zentralblatt MATH identifier
0858.62037

Citation

Deheuvels, Paul; Einmahl, John H. J. On the strong limiting behavior of local functionals of empirical processes based upon censored data. Ann. Probab. 24 (1996), no. 1, 504--525. doi:10.1214/aop/1042644729. https://projecteuclid.org/euclid.aop/1042644729


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