The Annals of Statistics

A Histogram Estimator of the Hazard Rate with Censored Data

Regina Y. C. Liu and John Van Ryzin

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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

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

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


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

Censored data hazard function histogram method consistency asymptotic normality


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.

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