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題名 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作者 黃品勝 貢獻者 鄭宗記
黃品勝關鍵詞 馬氏距離
遺漏值
混合資料
多重插補
Mahalanobis distances
missing value
mixed data
multiple imputation日期 2016 上傳時間 20-Jul-2016 16:52:21 (UTC+8) 摘要 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.參考文獻 Bar-Hen, A. and Daudin, J. J. (1995). Generalization of the Mahalanobis Distance in The Mixed Case. Journal of Multivariate Analysis, 53, 332-342 Bedrick, E. J., Lapidus, J. and Powell, J. F. (2000). Estimating the Mahalanobis Dista- Nce from Mixed Continuous and Discrete Data. Biometric 56, 394-401. Byar, D. P., Green S. B. (1980). The choice of treatment for patients based on covari- ate information: application to prostate cancer. Bull du Cancer 67,477-490 Dempster, A. P., Laird, M., Rubin, D. B. (1977). Maximum likelihood from incompl- Ete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39, 1-38 De Maesschalck, R., Jouan-Rimbaud, D. and Massart, D. L. (2000). The Mahalanobis Distance, Chemometrics and Intelligent Laboratory Systems 50, 1-18 Hunt L. and Jorgensen M. (1999). Mixture model clustering using the multimix progr- am. Australia and New Zealand Journal of Statistics 41,153-171 Schafer J. L. (1977). Analysis of Incomplete Multivariate Data, CHAPMAN and HA- LL Kullback, S. (1959). Information Theory and Statistical. New-York: Dover. Krzanowski, W. J. (1983). Distance between population using mixed continuous and categorical variable. Biometrika 70, 235-243 Kenne Pagiui, E. C. and Canale, A. (2014). Pairwise likelihood inference for multiva- Riate categorical responses. Technical Report, Department of Statistics, Univers- ity of Padua Little, R. J. A. and Rubin, D. B. (1989). The analysis of social science data with miss- ing values. Sociological Methods and Research, 18, pp. 292-326 Many, B. F. J. (1994). Multivariate Statistical Method: A Prime, 2nd edition. New Yo- rk : Chapman amd Hall. Mahalanobis, P. C.(1936). On the generalized distance in statistics, Proceedings of the National Institute of Science India, 2, 49–55. McParland,D.and Gormley,I.C. (2014). Model base clustering for mixed data:cluster- MD.Technical,University College Dublin. Olkin, I. and Tate, R. F. (1961). Multivariate correlation models with mixed discrete and continuous variables. Annals of Mathematical Statistics 32,448-465 Poon, W. Y. and Lee, S. Y. (1987). Maximum likelihood estimation of multivariate polychoric correlation coefficients. Psychometrika 52, 409-430. Rao, C. R (1973). Linear Statistic Inference and Its Applications, 2nd edition. New York :Wiley. Rubin, D. B. (1976). Inference and missing data. Biometrika 63, 581-592 Rubin, D. B. (1987). Multiple Imputations for Nonresponse in Surveys. Wiley, New York Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components. New York: Wiley. Scafer,J.L(1999). Multiple imputation: a primer. Statiscal methods in medical resear- ch, 8(1), 3-15 描述 碩士
國立政治大學
統計學系
103354017資料來源 http://thesis.lib.nccu.edu.tw/record/#G0103354017 資料類型 thesis dc.contributor.advisor 鄭宗記 zh_TW dc.contributor.author (Authors) 黃品勝 zh_TW dc.creator (作者) 黃品勝 zh_TW dc.date (日期) 2016 en_US dc.date.accessioned 20-Jul-2016 16:52:21 (UTC+8) - dc.date.available 20-Jul-2016 16:52:21 (UTC+8) - dc.date.issued (上傳時間) 20-Jul-2016 16:52:21 (UTC+8) - dc.identifier (Other Identifiers) G0103354017 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99311 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 103354017 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents 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 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103354017 en_US dc.subject (關鍵詞) 馬氏距離 zh_TW dc.subject (關鍵詞) 遺漏值 zh_TW dc.subject (關鍵詞) 混合資料 zh_TW dc.subject (關鍵詞) 多重插補 zh_TW dc.subject (關鍵詞) Mahalanobis distances en_US dc.subject (關鍵詞) missing value en_US dc.subject (關鍵詞) mixed data en_US dc.subject (關鍵詞) multiple imputation en_US dc.title (題名) 具遺漏值之連續與順序變數混合資料的馬氏距離估計 zh_TW dc.title (題名) Estimating of Mahalanobis distances for mixed continuous and ordinal data with missing values en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Bar-Hen, A. and Daudin, J. J. (1995). Generalization of the Mahalanobis Distance in The Mixed Case. Journal of Multivariate Analysis, 53, 332-342 Bedrick, E. J., Lapidus, J. and Powell, J. F. (2000). Estimating the Mahalanobis Dista- Nce from Mixed Continuous and Discrete Data. Biometric 56, 394-401. Byar, D. P., Green S. B. (1980). The choice of treatment for patients based on covari- ate information: application to prostate cancer. Bull du Cancer 67,477-490 Dempster, A. P., Laird, M., Rubin, D. B. (1977). Maximum likelihood from incompl- Ete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39, 1-38 De Maesschalck, R., Jouan-Rimbaud, D. and Massart, D. L. (2000). The Mahalanobis Distance, Chemometrics and Intelligent Laboratory Systems 50, 1-18 Hunt L. and Jorgensen M. (1999). Mixture model clustering using the multimix progr- am. Australia and New Zealand Journal of Statistics 41,153-171 Schafer J. L. (1977). Analysis of Incomplete Multivariate Data, CHAPMAN and HA- LL Kullback, S. (1959). Information Theory and Statistical. New-York: Dover. Krzanowski, W. J. (1983). Distance between population using mixed continuous and categorical variable. Biometrika 70, 235-243 Kenne Pagiui, E. C. and Canale, A. (2014). Pairwise likelihood inference for multiva- Riate categorical responses. Technical Report, Department of Statistics, Univers- ity of Padua Little, R. J. A. and Rubin, D. B. (1989). The analysis of social science data with miss- ing values. Sociological Methods and Research, 18, pp. 292-326 Many, B. F. J. (1994). Multivariate Statistical Method: A Prime, 2nd edition. New Yo- rk : Chapman amd Hall. Mahalanobis, P. C.(1936). On the generalized distance in statistics, Proceedings of the National Institute of Science India, 2, 49–55. McParland,D.and Gormley,I.C. (2014). Model base clustering for mixed data:cluster- MD.Technical,University College Dublin. Olkin, I. and Tate, R. F. (1961). Multivariate correlation models with mixed discrete and continuous variables. Annals of Mathematical Statistics 32,448-465 Poon, W. Y. and Lee, S. Y. (1987). Maximum likelihood estimation of multivariate polychoric correlation coefficients. Psychometrika 52, 409-430. Rao, C. R (1973). Linear Statistic Inference and Its Applications, 2nd edition. New York :Wiley. Rubin, D. B. (1976). Inference and missing data. Biometrika 63, 581-592 Rubin, D. B. (1987). Multiple Imputations for Nonresponse in Surveys. Wiley, New York Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components. New York: Wiley. Scafer,J.L(1999). Multiple imputation: a primer. Statiscal methods in medical resear- ch, 8(1), 3-15 zh_TW
