Ld. Brown et al., OPTIMAL CONFIDENCE SETS, BIOEQUIVALENCE, AND THE LIMACON OF PASCAL, Journal of the American Statistical Association, 90(431), 1995, pp. 880-889
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.