Asymptotically optimal procedures in multivariate Bayesian sequential estimation

ABSTRACT

In this article, we consider the problem of multivariate 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 than 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.

KEYWORDS:

• Asymptotically optimal
• asymptotically pointwise optimal
• multivariate Bayesian sequential estimation
• optimal sequential procedure
• robust

SUBJECT cLASSIFICATIONS:

• 62L12
• 62C10

Acknowledgment

The author thanks the Editor, Associate Editor, and referee for their helpful comments and suggestions.