Asymptotic theory for the MLE from randomly censored exponential samples

The MLE of the parameter of the exponential population from the censored observations is considered. The Edgeworth expansions for the Studentized MLE are established by representing the relevant statistic as a U-statistic plus a remainder. A semiparametric bootstrap method is introduced to the random censored model and the accuracy of bootstrap approximation of the MLE is investigated. Furthermore, it is shown that the MLE is asymptotically minimax efficient.