在 貝 氏 的 架 構 下 ， 考 慮 研 究 使 用 非 對 稱 的 LINEX(linear exponential) 損失函??估計一維指?族(one-parameter exponential family)分佈的平均值並且每個觀察值有一固定成本的序?估計問題。本研究計畫對LINEX 損失函?的貝氏序?估計問題，在給定事先分佈(prior distribution) 下， 提出二階段法則 (two-stage procedure)並證明它具有漸近點最優(asymptotically pointwise optimal)和漸近最佳(asymptotically optimal)性質。除此之外，將提出一個具有穩健性(robust)的二階段法則，此法則與資?的分佈、事先分佈無關，並將證明在某些條件下的事先分佈，它如同給定事先分佈下的漸近點最優法則所具有的漸近性質。 Within the framework of Bayesian model, we consider the problem of sequentially estimating the mean in one-parameter exponential family with an asymmetric LINEX (linear-exponential) loss function and fixed cost for each observation. Given a prior, a two-stage procedure is proposed and shown to be asymptotically pointwise optimal and asymptotically optimal. In addition, we propose a robust two-stage procedure, not depending on the distribution of outcome variable and the prior. It is shown that the procedure also shares the asymptotic properties with the asymptotically pointwise optimal rules for a large class of prior distributions.
