| 研究生: |
黃品勝 |
|---|---|
| 論文名稱: |
具遺漏值之連續與順序變數混合資料的馬氏距離估計 Estimating of Mahalanobis distances for mixed continuous and ordinal data with missing values |
| 指導教授: | 鄭宗記 |
| 學位類別: |
碩士
Master |
| 系所名稱: |
商學院 - 統計學系 Department of Statistics |
| 論文出版年: | 2016 |
| 畢業學年度: | 104 |
| 語文別: | 中文 |
| 論文頁數: | 38 |
| 中文關鍵詞: | 馬氏距離 、遺漏值 、混合資料 、多重插補 |
| 外文關鍵詞: | Mahalanobis distances, missing value, mixed data, multiple imputation |
| 相關次數: | 點閱:30 下載:0 |
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Bedrick, Lapodus和Powell(2000)提出利用常態潛在變數模型(normal latent variable model),估計連續與順序變數混合型資料(mixed data)馬氏距離(Mahalanobis Distance)的方法,在本論文中沿用相同方法來估計具遺漏值混合型資料馬氏距離,利用一般位置模型(general location model)進行多重插補(multiple imputation)的方法,藉由模擬資料與實例分析,來評估此方法用於處理估計具遺漏值混合型資料馬氏距離。
Bedrick, Lapodus, and Powell(2000) apply the normal latent variable model to estimate the Mahalanobis distances for mixed continuous and ordinal data. In this thesis, we extend the similar idea by applying general location model and multiple imputation to estimate the Mahalanobis distances for mixed countinuous and ordinal data with missing value. Simulation and real data are used to evaluate the proposed method.
第一章 緒論1
1.1研究背景與動機………………………………………………………1
1.2研究目的………………………………………………………………2
1.3論文架構………………………………………………………………3
第二章 一般位置模型與多重插補4
2.1一般位置模型(general location model)與最大概似估量……………4
2.2 EM演算法……………………………………………………………5
2.2.1預測機率函數…………………………………………………6
2.2.2一般位置模型下EM演算法…………………………………8
2.3多重插補(multiple imputation)…………………………………………9
2.3.1多重插補統計推論……………………………………………9
第三章 估計混合型資料馬氏距離11
3.1混合型資料馬氏距(Mahalanobis distances)………………………11
3.2估計混合型資料馬氏距離……………………………………………13
3.3馬氏距離估計量統計推論……………………………………………15
第四章 估計具遺漏值混合型資料馬氏距離與模擬分析17
4.1具遺漏值時一般位置模型下多重插補的馬氏距離估計……………17
4.2模擬分析………………………………………………………………22
第五章 實例分析………………………………………………………………….29
第六章 結論與後續研究………………………………………………………….36
參考文獻…………………………………………………………………………37
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