Nonparametric Methods for Hazard Rate Estimation from Right-Censored Samples.
SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS AND STATISTICS
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Nonparametric estimation of the hazard rate or failure rate is a frequent topic of investigation in the statistical literature because of its practical importance. Until quite recently, hazard rate estimation had been based on complete samples of independent identically distributed lifetimes. However, observations may be censored or truncated in many life testing situations. This occurs often in medical trials when the patients may enter treatment at different times and then either die from the disease under investigation or leave the study before its conclusion. A similar situation may occur in industrial life testing when items are removed from the test at random times for various reasons. It is of interest to be able to estimate nonparametrically the unknown hazard rate of the lifetime random variable from this type of data without ignoring or discarding the right-censored information. The purpose of this paper is to discuss nonparametric estimation of the hazard rate function for right-censored samples. The various types of estimators that have been proposed in the literature will be indicated and briefly discussed in Section 3. These include maximum likelihood estimators, kernel type estimators, Bayesian estimators, and histogram estimators. Due to their computational simplicity and other properties, the kernel-type hazard rate estimators will be emphasized. Results of Tanner 1983 and Tanner and Wong 1983, 1984 will be presented in Section 4 while the estimator considered by McNichols and Padgett 1981 will be discussed in Section 5.
- Statistics and Probability