Asymptotic Properties of M-estimators Based on Estimating Equations and Censored Data

Properties of Huber's M-estimators based on estimating equations have been studied extensively and are well understood for complete (i.i.d.) data. Although the concepts of M-estimators and in ̄uence curves have been extended for some time by Reid (1981) to incomplete data that are subject to right censoring, results on the general behavior of Mestimators based on incomplete data remain scattered and restrictive. This paper establishes a general large sample theory for M-estimators based on censored data. We show how to extend any asymptotic result available for M-estimators based on complete data to the case of censored data. The extensions are usually straightforward and include the multiparameter situation. Both the lifetime and censoring distributions may be discontinuous. We illustrate several extensions which provide simple and tractable suf®cient conditions for an Mestimator to be strongly consistent and asymptotically normal. The in ̄uence curves and asymptotic variance of the M-estimators are also derived. The applicability of the new suf®cient conditions is demonstrated through several examples, including location and scale M-estimators.