The Annals of Statistics
- Ann. Statist.
- Volume 13, Number 2 (1985), 592-605.
A Histogram Estimator of the Hazard Rate with Censored Data
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.
Ann. Statist., Volume 13, Number 2 (1985), 592-605.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G05: Estimation
Secondary: 62P10: Applications to biology and medical sciences 62E20: Asymptotic distribution theory
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