Asymptotically pointwise optimal rules of sequential estimation of mean vector when an information matrix has some structure in a multivariate normal population

Abstract

The exact formulas of Bayes stopping times are often difficult to derive. Bickel and Yahav (1965) had provided the large sample approximation known as the "Asymptotically pointwise optimal" (A.P.O.) rule. The A.P.O. rule for the problem of the mean of a multivariate normal distribution, for a completely unknown covariance matrix , has been developed by the present author. This paper gives the A.P.O. rule of the mean of a multivariate normal ditribution for a covariance matrix with some structure. Also the result is shown to be asymptotically" non-deficient" in the sence of Woodroofe.

Keywords:

• A.P.O. rule
• covariance matrix
• conjugate distribution
• optional stopping theorem
• martingale
• martingale convergence theorem
• stopping rule
• intraclass correlation structure
• multivariate normal distribution