Asymptotically pointwise optimal rules for estimating the mean in general exponential dtstributions for squared loss

Abstract

Since exact formulae for Bayes stopping tirncs in sequential analysis are often difficult to derive.Bickle and Yahav considered an attractive large sample approximation known as " Asymptotically pointwise optimal" (A.P.O.) rulp. The (A.P.O.) rule. for the problem of cst the mean of a multivariate normal distribution has been treated by some authors but only for the case where the covariance matrix is scalar times a known matrix.In this paper, A.P.O. rules are given for a general exponeritial fitmily fror which the results for milltic,aria.tr norrnal mean vector with c-ompli.tely unknow covariance matrix are obtained. We also consider a multinomial distribution case.

Keywords:

• A.P.O. rule: general exponential distribution
• conjugate distribution
• optional theorem
• martingale
• stipping rule
• multinomial distribution
• multivariate nlormal distribution