The risks for usual sequential estimates and stopping times of multivariate normal mean for conjugate distribution

Abstract

The exact formulas of optimal stopping times for usual problems are often difficult to derive. Biekej and Yahav (1965) had provided the large sample approximation known as the asymptotically pointwise optimal (A. P.O.) rule. In Nagao (1997a.b). he has derived the asymptotic formulas for Bayes stopping times for the problems of the mean of a multivariate normal distribution when a covariance matrix is completely unknown and has some structure, respectively. This paper gives the risks for estimate and stopping times which we use in common for some problems. From this result, we find that its increasing amount shows the deficiency of estimate and stopping usually used from the view of the Bayes risk.