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題名 相容性條件隨機變數在插補上之應用
Applications of the compatible conditional random variables on imputation methods作者 曾琬甯 貢獻者 姜志銘
曾琬甯關鍵詞 插補
相容性日期 2011 上傳時間 10-May-2016 19:01:40 (UTC+8) 摘要 處理缺失之資料，已經有一些插補方法，但這些插補方法在不同情況下是否確實有效，仍有待探討pd Van Buuren et al.(2006) 對兩種不相容性模型 (一條件分配函數為線性，另一條件分配函數分別為平方及對數)進行討論，該論文依據模擬結果，僅表示在此兩不相容性模型下的插補方法似乎仍有效。本文則不僅嘗試解釋此兩模型為何有效，且進一步探討是否所有的不相容性模型插補後能與母體參數值相似而達到有效插補，並檢定其模擬後之結果，本文發現其答案為否定。
There are some available imputation methods to deal with missing data. However, whether imputation methods based on conditional distributions are effective is still questionable. Van Buuren et al.(2006) discuss two incompatible conditional distributions models (one conditional distribution has a linear relation, the other conditional distribution has a squared or a logarithmic relation). According to their simulation results, Van Buuren et al.(2006) conclude that imputation methods based on these two incompatible models are effective. In this thesis, we try to explain why the two imputation models are effective. In addition, we discuss whether all imputation methods based on incompatible models give estimated parameter values close to the true values. The simulation results of these methods are also tested statistically to answer this question. In conclusion, we find the answer is negative.
摘要 . . . . . . . . . . . . . . . . . . .1 Abstract . . . . . . . . . . . . . . . . 2 1 文獻回顧 .................................3 2 FCS插補法.................................5 2.1定義和介紹紹 . . . . . . . . . . 5 2.2 相容性 性 . . . . . . . . . . . .6 3 計算方法的介紹 .............................8 3.1 多元常態迴歸模型之建立立 . . . . . .8 3.2 吉氏抽樣器器 . . . . . . . . . . .10 4 相容性模型與不相容性模型之探討 ..........12 4.1 隨機遺失機制制 . . . . . . . . . . 12 4.2 模型之比較較 . . . . . . . . . . . 12 4.3 針對各種隨機遺失法插補後結果之討論討 . . . 16 5 檢定插補後資料之結果..................... .....30 5.1 適合度檢定法法 . . . . . . . . . . . 30 6 結論................................... 33 7 附錄.............................. 36參考文獻 [1] Arnold, B. C. and Press, S. J. (1989), "Compatible Conditional Distributions," Journal of the American Statistical Association, 84, 152-156. [2] Drechsler, J. and Rassler, S. (2008), "Does Convergence Really Matter?" Recent Advances in Linear Models and Related Areas, Shalabh and Heumann, eds, Physical-verlag, Heidelberg, Germany, 341-355. [3] Geman, S. and Geman, D. (1984), "Stochastic Relation, Gibbs Distribution and the Bayesian Restortion of Image," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741. [4] Little, R. J. A. and Rubin, D. B. (1987), "Statistical analysis with missing data," New York：Wiley. [5] Martinez, W. L. and Martinez, A. R. (2002), "Computational statistics handbook with MATLAB," Boca Raton, Fla. : Chapman and Hall/CRC. [6] Press, S. J. (2003), "Subjective and Objective Bayesian Statistics: Principles, Models, and Applications," (2nd ed) Hoboken, N.J: John Wiley and Sons. [7] Rubin, D. B. (1987), "Multiple imputation for nonresponse in surveys," New York: John Wiley. [8] Schafer, J. L. (1997), "Analysis of Incomplete Multivariate Data," London: Chapman Hall. [9] Van Buuren, S. (2007), "Multiple imputation of discrete and continuous data by fully conditional specication," Statistical Methods in Medical Research, 16, 219-242. [10] Van Buuren, S., Brand, J. P. L., Groothuis-Oudshoorn, C. G. M., and Ru- bin, D. B. (2006), "Fully conditional specication in multivariate imputation," Journal of Statistical Computation and Simulation, 76, 1049-1064. [11] Walpole, R. E., Myers, R. H., Myers, S. L., Ye, K. (2007), "Probability & Statistics for Engineers & Scientists," (8th ed) London: Prentice Hall. 3 描述 碩士
國立政治大學
應用數學系
97751012資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097751012 資料類型 thesis dc.contributor.advisor 姜志銘 zh_TW dc.contributor.author (Authors) 曾琬甯 zh_TW dc.creator (作者) 曾琬甯 zh_TW dc.date (日期) 2011 en_US dc.date.accessioned 10-May-2016 19:01:40 (UTC+8) - dc.date.available 10-May-2016 19:01:40 (UTC+8) - dc.date.issued (上傳時間) 10-May-2016 19:01:40 (UTC+8) - dc.identifier (Other Identifiers) G0097751012 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/96373 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 97751012 zh_TW dc.description.abstract (摘要) 處理缺失之資料，已經有一些插補方法，但這些插補方法在不同情況下是否確實有效，仍有待探討pd Van Buuren et al.(2006) 對兩種不相容性模型 (一條件分配函數為線性，另一條件分配函數分別為平方及對數)進行討論，該論文依據模擬結果，僅表示在此兩不相容性模型下的插補方法似乎仍有效。本文則不僅嘗試解釋此兩模型為何有效，且進一步探討是否所有的不相容性模型插補後能與母體參數值相似而達到有效插補，並檢定其模擬後之結果，本文發現其答案為否定。 zh_TW dc.description.abstract (摘要) There are some available imputation methods to deal with missing data. However, whether imputation methods based on conditional distributions are effective is still questionable. Van Buuren et al.(2006) discuss two incompatible conditional distributions models (one conditional distribution has a linear relation, the other conditional distribution has a squared or a logarithmic relation). According to their simulation results, Van Buuren et al.(2006) conclude that imputation methods based on these two incompatible models are effective. In this thesis, we try to explain why the two imputation models are effective. In addition, we discuss whether all imputation methods based on incompatible models give estimated parameter values close to the true values. The simulation results of these methods are also tested statistically to answer this question. In conclusion, we find the answer is negative. en_US dc.description.abstract (摘要) 摘要 . . . . . . . . . . . . . . . . . . .1 Abstract . . . . . . . . . . . . . . . . 2 1 文獻回顧 .................................3 2 FCS插補法.................................5 2.1定義和介紹紹 . . . . . . . . . . 5 2.2 相容性 性 . . . . . . . . . . . .6 3 計算方法的介紹 .............................8 3.1 多元常態迴歸模型之建立立 . . . . . .8 3.2 吉氏抽樣器器 . . . . . . . . . . .10 4 相容性模型與不相容性模型之探討 ..........12 4.1 隨機遺失機制制 . . . . . . . . . . 12 4.2 模型之比較較 . . . . . . . . . . . 12 4.3 針對各種隨機遺失法插補後結果之討論討 . . . 16 5 檢定插補後資料之結果..................... .....30 5.1 適合度檢定法法 . . . . . . . . . . . 30 6 結論................................... 33 7 附錄.............................. 36 - dc.description.tableofcontents 摘要 . . . . . . . . . . . . . . . . . . .1 Abstract . . . . . . . . . . . . . . . . 2 1 文獻回顧 .................................3 2 FCS插補法.................................5 2.1定義和介紹紹 . . . . . . . . . . 5 2.2 相容性 性 . . . . . . . . . . . .6 3 計算方法的介紹 .............................8 3.1 多元常態迴歸模型之建立立 . . . . . .8 3.2 吉氏抽樣器器 . . . . . . . . . . .10 4 相容性模型與不相容性模型之探討 ..........12 4.1 隨機遺失機制制 . . . . . . . . . . 12 4.2 模型之比較較 . . . . . . . . . . . 12 4.3 針對各種隨機遺失法插補後結果之討論討 . . . 16 5 檢定插補後資料之結果..................... .....30 5.1 適合度檢定法法 . . . . . . . . . . . 30 6 結論................................... 33 7 附錄.............................. 36 zh_TW dc.format.extent 4418928 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097751012 en_US dc.subject (關鍵詞) 插補 zh_TW dc.subject (關鍵詞) 相容性 zh_TW dc.title (題名) 相容性條件隨機變數在插補上之應用 zh_TW dc.title (題名) Applications of the compatible conditional random variables on imputation methods en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Arnold, B. C. and Press, S. J. (1989), "Compatible Conditional Distributions," Journal of the American Statistical Association, 84, 152-156. [2] Drechsler, J. and Rassler, S. (2008), "Does Convergence Really Matter?" Recent Advances in Linear Models and Related Areas, Shalabh and Heumann, eds, Physical-verlag, Heidelberg, Germany, 341-355. [3] Geman, S. and Geman, D. (1984), "Stochastic Relation, Gibbs Distribution and the Bayesian Restortion of Image," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741. [4] Little, R. J. A. and Rubin, D. B. (1987), "Statistical analysis with missing data," New York：Wiley. [5] Martinez, W. L. and Martinez, A. R. (2002), "Computational statistics handbook with MATLAB," Boca Raton, Fla. : Chapman and Hall/CRC. [6] Press, S. J. (2003), "Subjective and Objective Bayesian Statistics: Principles, Models, and Applications," (2nd ed) Hoboken, N.J: John Wiley and Sons. [7] Rubin, D. B. (1987), "Multiple imputation for nonresponse in surveys," New York: John Wiley. [8] Schafer, J. L. (1997), "Analysis of Incomplete Multivariate Data," London: Chapman Hall. [9] Van Buuren, S. (2007), "Multiple imputation of discrete and continuous data by fully conditional specication," Statistical Methods in Medical Research, 16, 219-242. [10] Van Buuren, S., Brand, J. P. L., Groothuis-Oudshoorn, C. G. M., and Ru- bin, D. B. (2006), "Fully conditional specication in multivariate imputation," Journal of Statistical Computation and Simulation, 76, 1049-1064. [11] Walpole, R. E., Myers, R. H., Myers, S. L., Ye, K. (2007), "Probability & Statistics for Engineers & Scientists," (8th ed) London: Prentice Hall. 3 zh_TW
