M-ESTIMATORS FOR CENSORED-DATA - STRONG CONSISTENCY

Let ($) over cap F-n(x) denote the Kaplan-Meier product-limit estimate for the life distribution function F(x;theta(0)) based on randomly ce nsored data. The M-estimator of theta(0) corresponding to a function r ho is defined to be the value of theta which minimizes integral rho(x; theta) d ($) over cap F-n(x). The strong consistency of M-estimators i s studied. It is shown that most of the classical sufficient condition s based on rho, such as Wald (1949), Kiefer and Wolfowitz (1956) and H uber (1967), can be extended to randomly censored data. Two such exten sions based on Perlman (1972) and Wang (1985) are illustrated in detai l and applied to parametric, semi- and non-parametric classes.