Abstract: A generalized Bayes confidence estimator with respect to the Lebesgue prior is constructed for Fieller's confidence set. It is compared with the confidence coefficient under squared error loss. Besides its admissibility proved in Tsao and Hwang (1997), is shown to dominate the confidence coefficient, under some conditions, when dimension is 2 or 3. For large , it is shown that the domination fails. Numerical integration suggests that fails to dominate when . The results seem surprising.
Key words and phrases: Admissibility, domination, estimated confidence approach, Fieller's confidence set, generalized Bayes confidence estimator.