Estimation from Censored Data with Incomplete Information

Phillips and Sweeting [J. R. Statist. Soc. B 58 (1996) 775–783.] considered estimation of the parameter of the exponential distribution with censored failure time data when there is incomplete knowledge of the censoring times. It was shown that, under particular models for the censoring mechanism and censoring errors, it will usually be safe to ignore such errors provided they are not expected to be too large. A flexible model is introduced which includes the extreme cases of no censoring errors and no information on the censoring values. The effect of alternative assumptions about knowledge of the censoring values on the estimation of failure rate is investigated.