Asymptotic Optimal Estimation of Poisson Mean Under LINEX Loss Function

Abstract

In this article, we consider the problem of sequentially estimating the mean of a Poisson distribution under LINEX (linear exponential) loss function and fixed cost per observation within a Bayesian framework. An asymptotically pointwise optimal rule with a prior distribution is proposed and shown to be asymptotically optimal for arbitrary priors. The proposed asymptotically pointwise optimal rule is illustrated using a real data set.

Keywords:

• Asymptotically optimal
• Asymptotically pointwise optimal
• Bayes sequential estimation
• LINEX loss function
• Poisson distribution

Mathematics Subject Classification:

• Primary 62L12
• Secondary 62C10

Acknowledgments

The authors are grateful to the referees for their valuable comments. This research is partially supported by the National Science Council of R.O.C.