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. Alt hough the concepts of RI-estimators and influence 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 M-estimators based on incompl ete data remain scattered and restrictive. This paper establishes a general large sample theory for M-estimators based on censored data. We show how t o extend any asymptotic result available for M-estimators based on complete data to the case of censored data. The extensions are usually straightforw ard and include the multiparameter situation. Both the lifetime and censori ng distributions may be discontinuous. We illustrate several extensions whi ch provide simple and tractable sufficient conditions for an M-estimator to be strongly consistent and asymptotically normal. The influence curves and asymptotic variance of the M-estimators are also derived. The applicabilit y of the new sufficient conditions is demonstrated through several examples , including location and scale M-estimators.