Asymptotic Optimal Sequential Estimation: The Poisson Case

Abstract

The problems of estimating sequentially the intensity parameter of a homogeneous Poisson process and of estimating sequentially the mean of a sequence of i.i.d. Poisson rv's, are considered. The procedures suggested are shown to perform well for large values of the parameter and/or for small sampling cost. Having bounded regret, the procedure for estimating the mean of the Poisson sequence is asymptotically Bayes w.r.t. any sequence of a priori densities, which spread mass in a suitably smooth manner.