A PARADOX IN DECISION-THEORETIC INTERVAL ESTIMATION

Decision-theoretic interval estimation usually employs a loss function that is a linear combination of volume and coverage probability. Such loss functions, however, may result iu paradoxical behavior of Bayes rules. We investigate this paradox in the case of Student's t, and suggest ways of avoiding it using a different loss function. Some properties of the resulting Bayes rules are also examined. This alternative approach may also be generalized.