Abstract

This article compares a new piecewise exponential estimator (NPEE) of a survival function for censored data with other three famous estimators Kaplan-Meier estimator (KME), Nelson estimator (NE), and an empirical Bayes type estimator (EBE) found in the literature. The NPEE, which is continuous on [0;1), retains the spirit of the KME and provides an exponential tail with a hazard rate determined by a novel nonparametric consideration while the other three estimators have limited usage because of their various shortcomings. In our simulation study, we employed absolute bias and relative eciency as measures of quality of the models. We chose three levels of censoring and two sample sizes and did comparisons at various quantiles. It is found that the NPEE, which is asymptotically equivalent to the KME, is shown to be better than the other three estimators for finite samples.

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