Maximum Likelihood Estimation of the Survival Function Based on Censored Data Under Hazard Rate Assumptions

Abstract

Kiefer-woifowitz (1956) maximum likelihood estimators of the survival function are derived under the model assumptions of (a) increasing, (b) decreasing, and (c) U-shaped hazard rate based on right censored data. A strong consistency theorem is proved. Monte Carlo small sample comparisons are made with the maximum likelihood estimators based on the correct parametric model and the fully nonparametric maximum likelihood (product limit) esti-mator. Applications to covariate analysis are discussed. © 1981, Taylor & Francis Group, LLC. All rights reserved.