Conditional interval estimation of the extreme-value scale parameter following rejection of a pre-test

Abstract

A conditional confidence interval for the scale parameter of the extrernevalue distribution following a preliminary test is investigated. The conditional confidence interval (CCI) may be shorter than the unconditional confidence interval (UCI) in contrast to the findings for the mean of a normal distribution by Meeks and D'Agostino (1983). The conditional coverage probability of the UCI is obtained by computing the coverage probability under the conditional probability density function. It is shown that the conditional coverage probability of the UCI is not uniformly greater than or less than the nominal level. The UCI is appropriate only when one does not perform any pre-test. However, if a pre-test is performed before the constructicin of a confidence interval, then the appropriate confidence interval is the CCI because the pre-test affects subsequent inference procedures.