Buehler confidence limits and nesting

Abstract

The Buehler 1 - α upper confidence limit is as small as possible, subject to the constraints that its coverage probability is at least 1 - α and that it is a non-decreasing function of a pre-specified statistic T. This confidence limit has important biostatistical and reliability applications. Previous research has examined the way the choice of T affects the efficiency of the Buehler 1 - α upper confidence limit for a given value of α. This paper considers how T should be chosen when the Buehler limit is to be computed for a range of values of α. If T is allowed to depend on α then the Buehler limit is not necessarily a non-increasing function of α, i.e. the limit is 'non-nesting'. Furtherm..