OPTIMAL CONFIDENCE SETS, BIOEQUIVALENCE, AND THE LIMACON OF PASCAL

We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets ar e constructed by inverting a family of uniformly most powerful tests a nd hence they also enjoy the optimality property of being uniformly mo st accurate. In addition, these sets possess Bayesian optimal volume p roperties and represent the first case (to our knowledge) of a frequen tist l - alpha confidence set that possesses a Bayesian optimality pro perty. The hypothesis testing problem that generates these sets is sim ilar to that encountered in bioequivalence testing. Our sets are optim al for testing bioequivalence in certain settings; in the case of the normal distribution, the optimal set is a curve known as the limacon o f Pascal. We illustrate the use of these curves with a biopharmaceutic al example.