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    Title: 隨機篩選下之經驗貝氏指數檢定
    Other Titles: Testing for Exponential Population Based on Randomly Censored Data via Empirical Bayes Approach
    Authors: 黃文濤
    Contributors: 淡江大學經營決策學系
    Keywords: 指數分佈;隨機篩選資料;逼近最適性;收斂速率;exponential population;randomly censored data;asymptotically optimal;convergence rate
    Date: 2009
    Issue Date: 2010-04-15 15:46:14 (UTC+8)
    Abstract: 在此半年計畫中,吾人考慮獨立隨機變數X 及Y ,其中X 為依循指數分佈, θ e−θ x ,考慮貝氏架構下,θ 依循先驗分佈π (θ )。若在此貝氏架構下,自(X ,π (θ ))取得 樣本n X ,..., X 1 ,及自Y 取得n Y ,...,Y 1 。而這些樣本i Y 觀測不到。設( ) n n n I = I X < Y 及 ( ) n n n Z = min X ,Y , 則觀測值為(I Z i n) i i , ; = 1,..., 。吾人基於此觀測值做統計檢定 0 0 H :θ ≥θ vs 1 0 H :θ <θ ( 0 θ 為某已知值)。考慮線性損失函數。在此計劃中吾人將 提出ㄧ貝氏檢定n δ 基於前n 筆資料及目前第n +1筆資料下,預計可証得n δ 檢定之風險 值以速率約為O(ln n / n)趨近於貝氏風險。此計劃中之先驗分佈π (θ )只具極寬鬆之條件。 In this half year project, we try to study an empirical Bayes testing problem in exponential distribution based on randomly censored data. We will propose an empirical Bayes test n δ which will be shown to be asymptotically optimal with rate around O(ln n / n) that the regret tends to zero, where n is the number of past data.
    Appears in Collections:[管理科學學系暨研究所] 研究報告

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