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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/60432
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/60432


    Title: 凸函數最佳化在統計問題上的應用
    Convex optimization: A statistical application
    Authors: 劉世凰
    Contributors: 薛慧敏
    郭訓志

    劉世凰
    Keywords: 凸函數最佳化
    互補差餘條件
    受限最大概似估計量
    Date: 2009
    Issue Date: 2013-09-05 15:10:45 (UTC+8)
    Abstract: 近年來,凸函數最佳化相關的理論與實務已漸趨完善並廣泛應用在各種不同的領域上。已知針對限制條件下之最大概似估計量(Maximum Likelihood Estimator,簡寫MLE)求解的統計問題,一般都是先求解在無限制條件下之全域最大概似估計量(global MLE),若所求得之解能滿足給定的限制條件時,則代表我們的確得到所要的結果;但若所求得之解不能滿足限制條件時,我們就必須考量於此限制條件下之求解區域的最大概似估計量(local MLE),而其計算通常趨於複雜。在本研究中,我們嘗試藉由凸函數最佳化的理論與方法在受限最大概似估計量的求解上。首先針對一組2X2列聯表(contingency table)資料,給定限制條件為勝算比(odds ratio,簡寫OR)不小於1情況下,欲求各聯合機率之受限最大概似估計量。接下來則討論針對3X2列聯表資料,給定兩個區域勝算比(local OR)皆不小於1之限制條件,求取各聯合機率的受限最大概似估計量。我們最終整理歸納出一套分析方法,並將此歸納結果拓展到對於任意J不小於2之JX2列聯表中之受限最大概似估計量計算問題上。本研究中所提出的求解方法包括將決策變數重新參數化,忽略原始的線性限制等式,並另外在原始目標問題中加入某個懲罰項,使其新的最佳化問題滿足凸函數最佳化問題的條件。接下來利用凸函數最佳化之理論,列出其Karush-Kuhn-Tucker 條件,再藉其中的互補差餘條件(complementary slackness)來分析求得理論最佳解。最後我們得出當懲罰項之相對應的係數為n時,則其所求得之最佳解即為此統計問題中之受限最大概似估計量。
    Reference: 一、英文文獻
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    二、中文文獻
    1. 廖慶榮(2006),作業硏究,華泰文化。
    Description: 碩士
    國立政治大學
    統計研究所
    97354014
    98
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0097354014
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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