臺灣博碩士論文加值系統

貝氏序列所探討的估計問題,是為了找尋一個最佳的序列法則,此最佳的序列法則即為最佳的決策。其中最佳序列法則包含最佳停止時間和貝氏估計量。通常貝氏估計量是可以被找出來的,但是最佳停止時間通常無法被明確的表示出,所以大部分的文獻針對所提出的停止時間討論其漸近性質,並比較它的貝氏風險與最佳停止時間的貝氏風險兩者的值。在非貝氏的觀點上,如Robbins(1959)所發表的論文,在常態母體下,對於sigma未知時,用樣本平均數估計mu,給定一序列法則並討論比較最佳固定樣本數的風險,然而 Ghosh 和 Mukhopadhyay (1981) 則延續 Robbins 所提出的相關問題,改以二階段抽樣法則來代替序列估計方法,探討二階段抽樣法則中漸近有效性的相關問題,藉由上述的非貝氏序列估計觀念,我們加入貝氏的觀念來導引出本文。在 Hwang (1999b) 的論文中,以指數分佈為例,在一些已知條件下,探討貝氏序列下二階段抽樣法的貝氏風險與最佳序列法則的貝氏風險的比值靠近1。而本文是建構在貝氏的觀點上,所以我們參照 Hwang (1999b) 所發表的論文來建構本文,而本文主要在討論常態分佈下貝氏序列估計之二階段抽樣法,考慮在先驗分佈未知的情況下,證明出這樣所得到的貝氏風險與最佳固定樣本數的貝氏風險比值會小於1。

The Bayes sequential estimation problem is to seek an optimal sequential procedure which includes an optimal stopping time and a Bayes estimator. The Bayes estimator is always obtained in the problem, and the optimal stopping time exists, but the exact determination of the optimal stopping time appears to be a formidable task, in practice. There are many papers that discussed the asymptotic efficiency for the proposed stopping time, and its Bayes risk compare to Bayes risk of optimal stopping time.In the classical non-Bayesian sequential estimation problem, Robbins (1959) proposed a sequential procedure and compared its Bayes risk with the Bayes risk 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. Hwang (1999b) proposed a two-stage procedure to Bayes sequential estimation in the exponential distribution, and proved that the ratio of Bayes risk of the proposed procedure and the Bayes risk of the optimal sequential procedure goes to one as c approaches zero under some conditions. A two-stage procedure, not depending on the prior distribution, for the normal case is proposed in this paper. It is shown that the ratio of Bayes risk of the proposed two-stage procedure and the Bayes risk of the optimal fixed sample size procedure is asymptotically smaller than one.

目 錄
第一章 緒論
第1.1節 研究動機與目的.........................................1
第1.2節 章節架構...............................................2
第二章 最佳固定樣本數與二階段抽樣法
第2.1節 固定樣本大小下的貝氏風險...............................3
第2.2節 二階段抽樣法的介紹.....................................4
第三章 二階段抽樣法的主要結果.................................6
第四章 最佳固定樣本數與二階段抽樣法的模擬
第4.1節 資料的產生............................................15
第4.2節 模擬的方法............................................15
第4.3節 模擬的結果............................................16
第五章 總結..................................................25
附錄 26
參考文獻 29

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