Two Stage Approach to Bayes Sequential Estimation in the Exponential Distribution

• Main Authors: Hwang, Bang-Hwang, 黃榜煌
• Other Authors: Hwang Leng-Cheng
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/03593077172527607183

碩士 === 淡江大學 === 數學學系 === 86 === The Bayes sequential estimation problem is to seek an optimal sequential procedure Which includes an optimal stopping time and a Bayes estimator. (i.e. the posterior mean of θ for square error loss.) The problem of determining optimal stopping rules is usually more formidable, and although such stopping rules exist under fairly general conditions, their exact determination is usually very difficult. There are many papers that discussed the optimal stopping time. For example, Chow, Robbins and Siegmund (1971) proved the existence of the optimal stopping time for a Bayes sequential estimation problem. Alvo (1977) obtained a lower bound for a Bayes risk of optimal stopping rules for one-parameter exponential family. Of course, there are many papers that discussed the asymptotic efficiency for the stopping time. That is, its Bayes risk compare to the Baye riskof optimal stopping time. In the classical non-Bayesian sequential estimation, Robbins (1959) proposed a sequential procedure and compared its Bayes risk with the Bayes of the optimal fixed sample size procedure in normal case. Replacing of fully sequential procedure, a two stage procedure is given by Ghosh and Mukhopadyay (1981). The asymptotic properties of the two stage procedure were discussed. In the Bayes sequential estimation problem the optimal fixed sample size procedure depends on prior distribution. In case the prior distribution is misspecified, unknown or irrelevant to the present θ, the optiaml fixed sample size can not be obtained. Hwang (1997) proposed a naive sequential procedure and did not depend on the prior distribution such that its Bayes risk was not greater than its Bayes risk of optimal fixed sample size procedure. Instead of the sequential procedure in Hwang (1997), a two stage procedure is proposed in the present paper. The asymptotic properties of procedure are the same as the sequential procedure proposed by Hwang (1997),a two stage procedure is proposed in the present paper. The asymptotic properties of procedure are the same as the sequential procedure proposed by Hwang (1997).