Abstract
This chapter presents the different types of nonparametric density estimates that have been proposed for the situation that the sample data are censored or incomplete. It is of interest to be able to estimate nonparametrically the unknown density of the lifetime random variable from this type of data without ignoring or discarding the right-censored information. The various types of estimators from right-censored samples that have been proposed include histogram-type estimators, kemel-type estimators, maximum likelihood estimators, Fourier series estimators, and Bayesian estimators. As the hazard rate function estimation problem is closely related to the density estimation problem, various types of nonparametric hazard rate estimators from right-censored data are mentioned. Because of their computational simplicity and other properties, the kernel-type density estimators are emphasized, and some examples are presented.
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