Asymptotically optimal procedures in multivariate Bayesian sequential estimation

In this article, we consider the problem of multivartate Bayesian sequential estimation of the unknown mean vector. We propose a robust sequential procedure without using the prior information or any auxiliary data, which is similar to multivariate non-Bayesian sequential estimation by M. Ghosh et al. (1976). The proposed procedure, depending only on the present data but not on its distribution, is shown to be asymptotically as well as or better tban the optimal fixed -sample -size procedures for the arbitrary distributions and asymptotically pointwise optimal and asymptotically optimal for multivariate exponential family with a large class of prior distributions.