M-ESTIMATORS FOR CENSORED-DATA - STRONG CONSISTENCY

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