ROBUST ESTIMATION UNDER TYPE II CENSORING

The properties of robust M‐estimators with type II censored failure time data are considered. The optimal members within two classes of ψ‐functions are characterized. The first optimality result is the censored data analogue of the optimality result described in Hampel et al. (1986); the estimators corresponding to the optimal members within this class are referred to as the optimal robust estimators. The second result pertains to a restricted class of ψ‐functions which is the analogue of the class of ψ‐functions considered in James (1986) for randomly censored data; the estimators corresponding to the optimal members within this restricted class are referred to as the optimal James‐type estimators. We examine the usefulness of the two classes of ψ‐functions and find that the breakdown point and efficiency of the optimal James‐type estimators compare favourably with those of the corresponding optimal robust estimators. From the computational point of view, the optimal James‐type ψ‐functions are readily obtainable from the optimal ψ‐functions in the uncensored case. The ψ‐functions for the optimal robust estimators require a separate algorithm which is provided. A data set illustrates the optimal robust estimators for the parameters of the extreme value distribution.