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    Title: LASSO於羅吉斯迴歸模型之估計的應用
    Application of LASSO Estimation of a Logistic Regression Model
    Authors: 鍾其昀
    Contributors: 薛慧敏
    鍾其昀
    Keywords: 最小平方法
    最大概似估計
    Date: 2017
    Issue Date: 2017-02-08 16:32:56 (UTC+8)
    Abstract: 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。
    Reference: 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。
    Description: 碩士
    國立政治大學
    統計學系
    103354015
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0103354015
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

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