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Abstract
This article examines how the level of censoring affects the validity of confidence intervals constructed from an exponential maximum likelihood estimator under departures from an assumed exponential survival distribution. The motivation for this work is a simulation study by Emerson (1981) suggesting that under Weibull departures from exponentiality, validity of confidence intervals for median survival time improves as censoring increases. To see if this result holds asymptotically in the case of complete censoring, first conditions are found under which the exponential maximum likelihood estimate of a percentile is asymptotically normal uniformly in F, where F is an arbitrary survival distribution function. Then, the asymptotic coverage probability of the exponential-based interval is found for a percentile of a local alternative to the exponential distribution. If the censoring distribution converges weakly to point mass at 0, and if the departure from exponentiality is independent of the censoring distribution, then the asymptotic coverage probability converges to the expected coverage probability under exponentiality. The least favorable direction of departure from exponentiality is found, and it is shown by counterexample that in the limiting case of complete censoring, if the departure from exponentiality depends on the censoring distribution as it does in the least favorable case, then the asymptotic coverage probability does not necessarily converge to the expected coverage probability under exponentiality. Finally, the results of this article are applied to uniformly censored Weibull alternatives, and the asymptotic-theory coverage probabilities are compared with simulated coverage probabilities.
