Statistical inference for bounds of random variables

Robson & Whitlock (1964) considered point estimation and confidence limits for the upper bound of a random variable when the bound was known to be a truncation point. However, their approach to the point estimation problem failed to produce an estimator with smaller mean squared error than the largest order statistic from a random sample. In this paper we construct point estimators of the bounds of random variables which are substantially better estimators than the extreme order statistics for many classes of random variables, including those whose distributions are truncated at one or both ends. We also construct confidence limits and tests of hypotheses for bounds. The main results are large sample results.