ASYMPTOTICALLY POINTWISE OPTIMAL RULES IN THE POISSON PROCESS

Abstract

The concept of asymptotic pointwise optimality in the discrete time processes provided by Bickel and Yahav (1967) is extended to the continuous time processes in the present paper. An asymptotically pointwise optimal (A.P.O.) rule is proposed in the homogeneous Poisson process. It is shown to be asymptotically optimal for the arbitrary priors and asymptotically non-deficient for the conjugate priors, expanding the discrete time processes of Bickel and Yahav (1968) and Woodroofe (1981) to accommodate the continuous time processes, respectively.

Keywords:

• Asymptotically non-deficient
• Asymptotically optimal
• Asymptotically pointwise optimal
• Bayes sequential estimation
• Homogeneous Poisson process

ACKNOWLEDGMENTS

Part of this work was supported by the National Science Council, R.O.C. The author is very grateful to the Editor and the referee for their valuable comments.