| Abstract: | For a multivariate normal distribution with unknown mean vector and unknown dispersion matrix, a sequential procedure for estimating the unknown mean vector is suggested. The procedure is shown to be asymptotically “risk efficient” in the sense of Starr (Ann. Math. Statist. (1966), 1173–1185), and the asymptotic order of the “regret” (see Starr and Woodroofe, Proc. Nat. Acad. Sci. 63 (1969), 285–288) is given. Moderate sample behaviour of the procedure using Monte-Carlo techniques is also studied. Finally, the asymptotic normality of the stopping time is proved. |
