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研究生:薛慧敏
研究生(外文):H. M. Hsueh
論文名稱:使用替代資料做羅吉斯模型的統計推論
指導教授:鄭光甫鄭光甫引用關係
指導教授(外文):K. F. Cheng
學位類別:博士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:中文
論文頁數:80
中文關鍵詞:替代資料錯誤分類錯誤測量羅吉斯模型最大估計概似法score檢定統計量
外文關鍵詞:surrogatemisclassificationmeasurement errorlogistic regression modelmaximum estimated likelihood estimatorscore test
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在羅吉斯迴歸模型下,若無法取得資料的準確測量值時,即二元反應變數可能有錯誤分類,解釋變數有測量誤差存在時,本文針對迴歸參數估計及
模型適合度檢定問題,提出數個合理可行的統計量。此時我們考慮雙重抽樣設計,在此法下則可取得一有效子樣本。由於有效樣本的存在,使我們可以取得錯誤分類及錯誤測量之資訊,且作適當之修正調整。
在迴歸參數的估計上,我們提出一最大估計概似法。則無論對錯誤分類及錯誤測量是否有額外資訊(如,此些機率服從某參數模型),皆可以分別以參數法或無母數法來估計此些干擾參數。在適當條件成立下,我們證明此些估計量之漸近常態性,且也討論此些估計量的漸近效率。尤其針對以無母數方法估計干擾參數下的最大概似估計法,證明在合理的條件下,此法有較高的漸近效率。
再者,我們針對羅吉斯迴歸模型的適合度檢定問題,討論由四個函數族個別推導出的score檢定量。此些檢定方法避免了以往以主觀的分群方法或是複雜的無母數方法來解決連續型解釋變數所產生的問題。另外我們並針對雙重抽樣樣本,適當的調整上述檢定統計量,提出估計score檢定統計量並推導其漸近變異矩陣。
透過模擬,我們比較在各種錯誤分類/錯誤測量模型下,上述迴歸參數各估計量及適合度檢定各估計score檢定統計量之有限樣本的性質。我們發現在各錯誤分類/錯誤測量模型下,最大估計概似法之表現不錯,而估計score檢定量與完整資料下所推導之score檢定量有相近的表現。
封面
摘要
誌謝辭
目錄
第一章 緒論
第二章 迴歸參數的估計
2.1 最大估計概似法(MEL)
2.2 錯誤分類下之漸近效率
2.3 錯誤測量下之漸近效率
2.4 迴歸參數估計的模擬研究
第三章 迴歸模型的適合度檢定
3.1 Score 檢定統計量
3.2 函數族介紹
3.3 適合度檢定的模擬研究
第四章 結論
附錄
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