Empirical bayes approach to bayes sequential estimation: the poisson and bernoulli cases

Abstract

The problem considered is the Bayes sequential estimation of the mean with quadratic loss and fixed cost per observation. Assume the prior distribution is not completely known. Some empirical Bayes procedures are proposed in the Poisson and Bernoulli cases, and they are shown to be asymptotically non-deficient in the sense of Woodroofe (1981).