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題名 相依資料的條件獨立檢定
A conditional independence test for dependent data
作者 鄭宇翔
Cheng, Yu Hsiang
貢獻者 黃子銘
Huang, Tzee Ming
鄭宇翔
Cheng, Yu Hsiang
關鍵詞 條件獨立檢定
日期 2012
上傳時間 2-Sep-2013 15:35:46 (UTC+8)
摘要 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。
參考文獻 [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.
描述 博士
國立政治大學
統計研究所
96354501
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096354501
資料類型 thesis
dc.contributor.advisor 黃子銘zh_TW
dc.contributor.advisor Huang, Tzee Mingen_US
dc.contributor.author (Authors) 鄭宇翔zh_TW
dc.contributor.author (Authors) Cheng, Yu Hsiangen_US
dc.creator (作者) 鄭宇翔zh_TW
dc.creator (作者) Cheng, Yu Hsiangen_US
dc.date (日期) 2012en_US
dc.date.accessioned 2-Sep-2013 15:35:46 (UTC+8)-
dc.date.available 2-Sep-2013 15:35:46 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2013 15:35:46 (UTC+8)-
dc.identifier (Other Identifiers) G0096354501en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/59282-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 96354501zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.tableofcontents 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		zh_TW
dc.format.extent 992071 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096354501en_US
dc.subject (關鍵詞) 條件獨立檢定zh_TW
dc.title (題名) 相依資料的條件獨立檢定zh_TW
dc.title (題名) A conditional independence test for dependent dataen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [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.		zh_TW