THE PROBABILITY THAT THE LARGEST OBSERVATION IS CENSORED

Suppose n possibly censored survival times are observed under an independent censoring model, in which the observed times are generated as the minimum of independent positive failure and censor random variables. A practical difficulty arises when the largest observation is censored since then the usual non-parametric estimator of the distribution of the survival time is improper. We calculate the probability that this occurs and give necessary and sufficient conditions for this probability to converge to 0 as n --> infinity. As an application, we show that if this probability is 0, asymptotically, then a consistent estimator for the mean failure time can be found. An almost sure version of the problem is also considered. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60 F05 SECONDARY 60 F15; 62 E20