Asymptotic Optimal Estimation of Poisson Mean Under LINEX Loss Function

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.