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| 研究生： |
鄭宇翔 Cheng, Yu Hsiang |
|---|---|
| 論文名稱： |
相依資料的條件獨立檢定 A conditional independence test for dependent data |
| 指導教授： |
黃子銘
Huang, Tzee Ming |
| 學位類別： |
博士
Doctor |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2013 |
| 畢業學年度： | 101 |
| 語文別： | 中文 |
| 論文頁數： | 45 |
| 中文關鍵詞： | 條件獨立檢定 |
| 相關次數： | 點閱：203 下載：24 |
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在一個考慮多個變數的問題中，變數間是否為條件獨立常是人們關心的議題。Huang[10]曾提出一個適用於IID資料的條件獨立檢定方法，此論文將說明此統計量亦適用於alpha-mixing資料的條件獨立檢定問題。另外本論文亦將考慮當條件變數為離散時的條件獨立檢定。本文證實藉由適當修正Huang的檢定統計量，則可解決上述資料型態的條件獨立檢定問題，另外文中亦會提供此修正統計量在條件獨立下的收斂性質。最後我們將利用模擬研究及實際資料分析來說明上述方法的表現。
1 簡介 1
2 文獻探討 4
2.1 獨立性檢定 ........................................ 4
2.2 條件獨立檢定 .......................................8
3 研究方法 11
3.1 非線性條件相關及其近似 ..............................11
3.2 非線性條件相關的估計及Huang之檢定統計量 ...............13
3.3 相依資料之條件獨立檢定 ..............................14
3.4 Z為離散隨機變數 ................................... 17
4 模擬研究 22
4.1 第一部分模擬研究 ...................................22
4.2 第二部分模擬研究 ...................................26
5 資料分析 32
6 證明 35
6.1 LEMMA 1證明 ..................................... 35
6.2 THEOREM 2證明 ................................... 37
6.3 THEOREM 3證明 ................................... 39
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