Statistica Sinica 9(1999), 795-810

GENERALIZED BAYES CONFIDENCE ESTIMATORS

FOR FIELLER'S CONFIDENCE SETS

C. Andy Tsao and J. T. Gene Hwang

Dong Hwa University and Cornell University

Abstract: A generalized Bayes confidence estimator $\gamma_L$ with respect to the Lebesgue prior is constructed for Fieller's confidence set. It is compared with the confidence coefficient $\gamma$ under squared error loss. Besides its admissibility proved in Tsao and Hwang (1997), $\gamma_L$ is shown to dominate the confidence coefficient, under some conditions, when dimension $p$ is 2 or 3. For large $p$, it is shown that the domination fails. Numerical integration suggests that $\gamma_L$ fails to dominate $\gamma$ when $p \geq 4$. The results seem surprising.

Key words and phrases: Admissibility, domination, estimated confidence approach, Fieller's confidence set, generalized Bayes confidence estimator.