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June, 1985 A Histogram Estimator of the Hazard Rate with Censored Data
Regina Y. C. Liu, John Van Ryzin
Ann. Statist. 13(2): 592-605 (June, 1985). DOI: 10.1214/aos/1176349541


A histogram type estimator of the hazard rate of lifetimes which are randomly right-censored is studied. This estimator is based on random spacings of the order statistics of uncensored observations and extends the idea of the histogram density estimation suggested by Van Ryzin (1973) to censored data. In this paper we establish pointwise large sample properties of the estimator including strong consistency, strong uniform consistency on a bounded interval, and two asymptotic distribution results. Of particular interest is the distribution result obtained by imposing extra "symmetry" conditions on the interval covering the given point. In fact, it yields the best attainable rate of convergence among all nonnegative estimators. Comparisons of our results with the kernel type estimators proposed in the literature are also given.


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Regina Y. C. Liu. John Van Ryzin. "A Histogram Estimator of the Hazard Rate with Censored Data." Ann. Statist. 13 (2) 592 - 605, June, 1985.


Published: June, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0612.62059
MathSciNet: MR790559
Digital Object Identifier: 10.1214/aos/1176349541

Primary: 62G05
Secondary: 62E20, 62P10

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 2 • June, 1985
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