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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 Ming en_US dc.contributor.author (Authors) 鄭宇翔 zh_TW dc.contributor.author (Authors) Cheng, Yu Hsiang en_US dc.creator (作者) 鄭宇翔 zh_TW dc.creator (作者) Cheng, Yu Hsiang en_US dc.date (日期) 2012 en_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) G0096354501 en_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) 96354501 zh_TW dc.description (描述) 101 zh_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 ................................... 174 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 ...................................265 資料分析 326 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/#G0096354501 en_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 data en_US dc.type (資料類型) thesis en 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
