The Annals of Statistics

A Histogram Estimator of the Hazard Rate with Censored Data

Regina Y. C. Liu and John Van Ryzin

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 592-605.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349541

Digital Object Identifier
doi:10.1214/aos/1176349541

Mathematical Reviews number (MathSciNet)
MR790559

Zentralblatt MATH identifier
0612.62059

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62P10: Applications to biology and medical sciences 62E20: Asymptotic distribution theory

Keywords
Censored data hazard function histogram method consistency asymptotic normality

Citation

Liu, Regina Y. C.; Ryzin, John Van. A Histogram Estimator of the Hazard Rate with Censored Data. Ann. Statist. 13 (1985), no. 2, 592--605. doi:10.1214/aos/1176349541. https://projecteuclid.org/euclid.aos/1176349541


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