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題名 LASSO於羅吉斯迴歸模型之估計的應用
Application of LASSO Estimation of a Logistic Regression Model
作者 鍾其昀
貢獻者 薛慧敏
鍾其昀
關鍵詞 最小平方法
最大概似估計
日期 2017
上傳時間 8-Feb-2017 16:32:56 (UTC+8)
摘要 隨著資料量龐大，解釋變數過多的時代來臨，變數選取將是我們重要的議題。在線性迴歸分析中，傳統採用最小平方法(least square method)來估計模型，然而得到的迴歸係數估計值的偏差雖然比較小，但其變異程度卻較大，且預測得也不夠精準。若是考慮對迴歸係數加入限制式時，則估計量將與原本的最小平方法有何差異，偏差與標準差之間的比較。接著將此估計法應用至羅吉斯迴模型時，利用三筆實際資料，比較與最大概似估計(maximum likelihood estimate，簡稱MLE)法建立的迴歸模型及預測準確率，並於模擬實驗中，以表格及圖型呈現兩方法在估計量上的差異。
參考文獻 一、英文文獻
1. Boyd, S. and Vandenberghe, L. (2004), Convex Optimization, Cambridge University Press, 215-244.
2. Breiman, L. (1995) Better Subset Regression Using the Nonnegative Garrotte, American Statistical Association, 37, 373-384.
3. Breiman, L. and Spector P. (1992) Submodel Selection and Evaluation in Regression. The X-Random Case,
International Statistical Review, 60, 291-319.
4. Dalal, N. Triggs, B. (2005) Histograms of Oriented Gradients for Human Detection, http://lear.inrialpes.fr/.
5. Friedl, I., Tilg, N. (1995) Variance estimates in logistic regression using the bootstrap, Communications in Statistic-Theory and Methods, 24(2), 473-486.
6. Hoerl, E. and Kennard, R. (1970) Ridge Regression: Biased Estimation for Nonorthogonal Problems, American Statistical Association, 12, 55-67.
7. Osborne, M., Presnell, B. and Turlach, B. (2000) On the LASSO and its dual, Journal of Computational and Graphical Statistics, 9, 319–337.
8. Sill, M.,Hielscher, T. A and Becker M. (2014) Extended Inference with Lasso and Elastic-Net Regularized Cox and Generalized Linear Models, Journal of Statistical Software, 62, 1-22.
9. Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso, Journal of the Royal Statistical Society, 58, 267-288.
10. Zhao, X. (2008) Lasso and Its Applications, University of Minnesota Duluth, 4-17.
11. Zou, H. and Hastie, T. (2005) Regularization and Variable Selection via the Elastic Net, Journal of the Royal Statistical Society, 67, 301-320.

二、中文文獻
1. 全民人體力學健康教室，淺談三種脊椎歪斜。
2. 賈金柱，高等統計選講，高等統計入門分析，2.2 節Duality。
描述 碩士
國立政治大學
統計學系
103354015
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0103354015
資料類型 thesis
dc.contributor.advisor 薛慧敏zh_TW
dc.contributor.author (Authors) 鍾其昀zh_TW
dc.creator (作者) 鍾其昀zh_TW
dc.date (日期) 2017en_US
dc.date.accessioned 8-Feb-2017 16:32:56 (UTC+8)-
dc.date.available 8-Feb-2017 16:32:56 (UTC+8)-
dc.date.issued (上傳時間) 8-Feb-2017 16:32:56 (UTC+8)-
dc.identifier (Other Identifiers) G0103354015en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/106389-
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) 103354015zh_TW
dc.description.abstract (摘要) 隨著資料量龐大，解釋變數過多的時代來臨，變數選取將是我們重要的議題。在線性迴歸分析中，傳統採用最小平方法(least square method)來估計模型，然而得到的迴歸係數估計值的偏差雖然比較小，但其變異程度卻較大，且預測得也不夠精準。若是考慮對迴歸係數加入限制式時，則估計量將與原本的最小平方法有何差異，偏差與標準差之間的比較。接著將此估計法應用至羅吉斯迴模型時，利用三筆實際資料，比較與最大概似估計(maximum likelihood estimate，簡稱MLE)法建立的迴歸模型及預測準確率，並於模擬實驗中，以表格及圖型呈現兩方法在估計量上的差異。zh_TW
dc.description.tableofcontents 1. 緒論..............................................1
2. 研究方法............................................3
2.1 線性迴歸之LASSO....................................3
2.2 羅吉斯迴歸之LASSO..................................14
3. 實例資料分析........................................15
3.1 脊椎後凸的預測.....................................15
3.2 貓與狗影像的辨識...................................18
3.3 鐵達尼號倖存者的預測................................21
4. 模擬實驗...........................................24
4.1 模擬流程與參數設計..................................24
4.2 估計量的比較.......................................25
5. 結論.............................................49
參考文獻..............................................50
附錄一(2.3)之推導證明..................................51
附錄二(2.3)之推導證明..................................52		zh_TW
dc.format.extent 934999 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103354015en_US
dc.subject (關鍵詞) 最小平方法zh_TW
dc.subject (關鍵詞) 最大概似估計zh_TW
dc.title (題名) LASSO於羅吉斯迴歸模型之估計的應用zh_TW
dc.title (題名) Application of LASSO Estimation of a Logistic Regression Modelen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 一、英文文獻
1. Boyd, S. and Vandenberghe, L. (2004), Convex Optimization, Cambridge University Press, 215-244.
2. Breiman, L. (1995) Better Subset Regression Using the Nonnegative Garrotte, American Statistical Association, 37, 373-384.
3. Breiman, L. and Spector P. (1992) Submodel Selection and Evaluation in Regression. The X-Random Case,
International Statistical Review, 60, 291-319.
4. Dalal, N. Triggs, B. (2005) Histograms of Oriented Gradients for Human Detection, http://lear.inrialpes.fr/.
5. Friedl, I., Tilg, N. (1995) Variance estimates in logistic regression using the bootstrap, Communications in Statistic-Theory and Methods, 24(2), 473-486.
6. Hoerl, E. and Kennard, R. (1970) Ridge Regression: Biased Estimation for Nonorthogonal Problems, American Statistical Association, 12, 55-67.
7. Osborne, M., Presnell, B. and Turlach, B. (2000) On the LASSO and its dual, Journal of Computational and Graphical Statistics, 9, 319–337.
8. Sill, M.,Hielscher, T. A and Becker M. (2014) Extended Inference with Lasso and Elastic-Net Regularized Cox and Generalized Linear Models, Journal of Statistical Software, 62, 1-22.
9. Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso, Journal of the Royal Statistical Society, 58, 267-288.
10. Zhao, X. (2008) Lasso and Its Applications, University of Minnesota Duluth, 4-17.
11. Zou, H. and Hastie, T. (2005) Regularization and Variable Selection via the Elastic Net, Journal of the Royal Statistical Society, 67, 301-320.

二、中文文獻
1. 全民人體力學健康教室，淺談三種脊椎歪斜。
2. 賈金柱，高等統計選講，高等統計入門分析，2.2 節Duality。		zh_TW