Robust estimation under progressive censoring

For progressively censored failure time data, the influence function and the breakdown point of robust M-estimators are derived. The most robust and the optimal robust estimators are also developed. The optimal members within two classes of ψ-functions are characterized. The first optimality result is the censored data analogue of the general optimality result. The second result pertains to a restricted class of ψ-functions. The usefulness of the two classes of ψ-functions is examined and it was found that the breakdown point and efficiency of the restricted class of optimal estimators compare favorably with those of the corresponding general optimal robust estimators. From the computational point of view, the restricted class of optimal ψ-functions are readily obtainable from the general optimal ψ-functions in the uncensored case. A data set illustrates the optimal robust estimators for the parameters of the extreme value distribution.