臺灣博碩士論文加值系統

貝氏序列估計目的在於找尋一個最佳序列法則（optimal sequential procedure），其中包含了最佳停止時間（optimal stopping time）與貝氏估計量（Bayes estimator），但是給出明確的最佳停止法則的形式經常是不容易的，所以Bickel and Yahav（1967﹐1968﹚提出大樣本近似的漸近點最優（asymptotically pointwise optimal）法則，來近似最佳停止時間。
本文主要探討在多維常態分佈下使用加權平方誤差損失加上抽樣成本的貝氏序列估計問題，這裡討論Hwang（2017）的穩健（robust）序列法則，以及Bickel and Yahav（1967﹐1968﹚所提出的大樣本漸近點最優法則，以上兩種方法都具備漸近最佳化性質，我們想討論比較在使用不同先驗分佈及參數設定下所得到的結果。
透過模擬本文在給定先驗分佈以及參數組合下，比較穩健型序列法則和漸進點最優序列法則之間的數值結果並進行討論，結果顯示在先驗分佈參數設定錯誤時，因為穩健型序列法則不受先驗分佈影響，而有較好的貝氏風險估計值。

The purpose of Bayesian sequence estimation is to find an optimal sequential procedure that includes the optimal stopping time and the Bayes estimator but gives the exact optimal stopping rule The form is often not easy, so Bickel and Yahav (1967, 1968) proposed the asymptotically pointwise optimal rule for large samples to approximate the optimal stopping time.
This article focuses on the Bayesian sequential estimation problem using weighted square error loss plus sampling cost under multidimensional normal distribution. We discuss the robust sequential procedure of Hwang (2017) and Bickel and Yahav (1967, 1968) Asymptotically pointwise optimal procedure for large samples, both of which have asymptotically optimal properties, we would like to discuss and compare the results of using different prior distribution and parameter settings.
In this article, we given a prior distribution and parameter combinations comparing the numerical results between the robust sequential procedure and the asymptotically pointwise optimal sequential procedure. The results show that when the a prior distribution parameters are set incorrectly the Bayesian risk estimation is better. Because the robust sequential procedure is not affected by the prior distribution.

目 錄
第一章 緒論 1
第二章 多維常態分配的貝氏序列估計 3
第三章 模擬分析及結果 6
第四章 結論 9
數值模擬表格 10
參考文獻 16

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