The efficiency of Buehler confidence limits

Abstract

The Buehler 1-α upper confidence limit is as small as possible, subject to the constraints that (a) its coverage probability never falls below 1-α and (b) it is a non-decreasing function of a designated statistic T. We provide two new results concerning the influence of T on the efficiency of this confidence limit. Firstly, we extend the result of Kabaila (Statist. Probab. Lett. 52 (2001) 145) to prove that, for a wide class of Ts, the T which maximizes the large-sample efficiency of this confidence limit is itself an approximate 1-α upper confidence limit. Secondly, there may be ties among the possible values of T. We provide the result that breaking these ties by a sufficiently small modif..