A robust asymptotically optimal procedure in Bayes sequential estimation

The problem of sequential estimation of the mean, subject to the loss defin ed as the sum of squared error loss and sampling costs, is considered withi n the Bayesian framework. It is shown that the sequential procedure, as pro posed by Chow and Yu (1981) in classical non-Bayesian sequential estimation , is, in fact, asymptotically Bayes for a large class of prior distribution s. The proposed procedure, without using any auxiliary data, is robust in t he sense that it does not depend on the distribution of outcome variables a nd the prior.