Dr. Mark F. Schilling (California State University Northridge)

Title: A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure

Abstract: The problem of obtaining a confidence interval for a binomial success parameter is one of the most common and basic of statistical situations. Despite the simplicity of the model and data structure, there is remarkable complexity to this problem. Existing procedures have been developed based on normal approximations, inversion of hypothesis tests, etc; the coverage probability function (cpf) of a given procedure is a key instrument for judging the adequacy of its performance. I will present a new procedure that is optimal in a fundamental sense, by employing an alternative approach: Choose the cpf optimally from the set of all possible cpfs, since stipulating the cpf is equivalent to specifying the confidence procedure. Performance of the procedure obtained from this approach is assessed both for the case when the confidence level represents a lower bound on coverage as well as for the situation when it is achieved only approximately. A new measure is introduced to help evaluate procedures in the latter case. Our procedure is compared to that of popular existing procedures on several measures and shown to be superior in essential ways.