在 貝 氏 的 架 構 下 ， 考 慮 研 究 使 用 非 對 稱 的 LINEX (linearexponential) 估計損失和抽樣成本的序?估計問題，Hwang and Lee (2011 b)提出給定事先分佈的漸近點最優(asymptotically pointwise optimal)法則具有漸近最佳(asymptotically optimal)性質，亦即具有最佳的一階次近似。本研究計劃針對常用的共軛事先(conjugate prior)分佈，分別討?特殊指?族分佈和一維指?族分佈的漸近點最優法則，將推導它們的貝氏風險至二階次近似，在某些條件下，將可得到漸近點最優法則具有如同Woodroofe (1981)的漸近最優(asymptotically non-deficient)性質。 Within the framework of Bayesian model, the problem of sequential estimation is considered under LINEX (linear-exponential) loss plus cost of sampling. In one-parameter exponential family, an asymptotically pointwise optimal procedure with a prior distribution is proposed and shown to be asymptotically optimal by Hwang and Lee (2011 b). In the project, natural conjugate prior distributions are assumed. The second order approximations to the Bayes risks of asymptotically pointwise optimal procedures will be obtained for the particular exponential family and the one-parameter exponential family, respectively. Then the asymptotically pointwise optimal procedures are shown to be asymptotically non-deficient in the sense of Woodroofe (1981), under some regularity conditions.
