簡易檢索 / 詳目顯示
| 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：204 下載：24 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
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
[1] Patrick Billingsley. Probability and Measure. John Wiley & Sons, New York, 1995.
[2] Taou.k Bouezmarni, Jeroen V. K. Rombouts, and Abderrahim Taamouti. A nonparametric copula based test for conditional independence with applications to Granger causality. Working papers, Departamento de Economia Universidad Carlos III de Madrid, 2009.
[3] Yu-Hsiang Cheng and Tzee-Ming Huang. A conditional independence test for dependent data based on maximal conditional correlation. Journal of Multivariate Analysis, 107:210–226, 2012.
[4] Jacques Dauxois and Guy Martial Nkiet. Nonlinear canonical analysis and independence tests. The Annals of Statistics, 26(4):1254–1278, 1998.
[5] David L. Banks (ed.), Campbell B. Read (ed.), and Samuel Kotz (ed.). Encyclopedia of Statistical Sciences (9 Vols. Plus Supplement), Volume S. John Wiley & Sons, 1989.
[6] Stephen E. Fienberg. The Analysis of Cross-classified Categorical Data. MIT Press, 1980.
[7] J. P. Florens and Denis Fougere. Noncausality in continuous time. Econometrica, 64(5):1195–1212, 1996.
[8] J. P. Florens and M. Mouchart. A note on noncausality. Econometrica, 50(3):583–591, 1982.
[9] Harold Hotelling. Relations between two sets of variates. Biometrika, 28:321– 377, 1936.
[10] Tzee-Ming Huang. Testing conditional independence using maximal nonlinear conditional correlation. The Annals of Statistics, 38(4):2047–2091, 2010.
[11] Anant M. Kshirsagar. Multivariate Analysis. Marcel Dekker, Inc., New York, 1972.
[12] Lexin Li, R. Dennis Cook, and Christopher J. Nachtsheim. Model-free variable selection. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 67(2):285–299, 2005.
[13] Oliver Bruce Linton and Pedro Gozalo. Conditional independence restrictions: Testing and estimation. Cowles Foundation Discussion Papers 1140, Cowles Foundation, Yale University, 1996.
[14] Roger B. Nelsen. An Introduction to Copulas. Springer, New York, 2006.
[15] Efstathios Paparoditis and Dimitris N. Politis. The local bootstrap for kernel estimators under general dependence conditions. Annals of the Institute of Statistical Mathematics, 52(1):139–159, 2000.
[16] Karl Pearson. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical
Magazine Series 5, 50(302):157–175, 1900.
[17] Larry L. Schumaker. Spline Functions: Basic Theory. Wiley-Interscience, New York, 1981.
[18] Liangjun Su and Halbert White. A consistent characteristic function-based test for conditional
independence. Journal of Econometrics, 141:807-834, 2007.
[19] Liangjun Su and Halbert White. A nonparametric Hellinger metric test for conditional independence.
Econometric Theory, 24(4):829–864, 2008.
[20] S. S. Wilks. Certain generalizations in the analysis of variance. Biometrika, 24:471–494, 1932.
