| 研究生: |
孟耿德 Meng, Geng De |
|---|---|
| 論文名稱: |
基於LASSO和FORWARD的節點選取方法比較 A comparison between two knot selection methods based on LASSO and FORWARD selection |
| 指導教授: |
黃子銘
Huang, Tzee Ming |
| 口試委員: |
翁久幸
Weng, Chiu-Hsing 黃貞瑛 Hwang, Jen-Ing |
| 學位類別: |
碩士
Master |
| 系所名稱: |
商學院 - 統計學系 Department of Statistics |
| 論文出版年: | 2017 |
| 畢業學年度: | 105 |
| 語文別: | 中文 |
| 論文頁數: | 15 |
| 中文關鍵詞: | 變數選取 、最小壓縮法 |
| 外文關鍵詞: | KNOT, LASSO |
| 相關次數: | 點閱:72 下載:0 |
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在無母數迴歸問題中,如果迴歸函數以spline函數近似,而且使用等距節點,則節點選取可以視為一個變數選取的問題。TiBshirani(1996)提出最小絕對壓縮挑選運算(Least Absolute Shrinkage and Selection Operator; LASSO)能夠對變數縮減,本研究中將考慮使用LASSO和forward 兩種選取變數方法進行節點選取。根據本研究模擬結果,forward選取方法的挑選節點效果比較好。
In nonparametric regression, if the regression function is approximated using a spline function with equally spaced knots ,then the problem of knot selection can Be considered as a variable selection problem. Tibshirani(1996) proposed Least Absolute Shrinkage and Selection Operator(LASSO), which can Be used for variable selection. In this thesis, two variable selection methods: LASSO and forward, are considered for knots selection. According to the simulation results in this thesis, the forward method is better for knot selection.
第一章 緒論 1
第二章 文獻迴顧 3
第三章 研究方法 4
第一節 模型假設與節點對應變數關係 4
第二節 LASSO運算 5
第四章 模擬和比較 7
第一節 節點設定 7
第二節 模擬比較 10
第五章 結論與建議 11
[1]Charles J. Stone(1997)Polynomial Splines and their Tensor Products in Extended Linear Modeling;p1374-p1377
[2]Denison, D., Mallick, B., and Smith, A. (1998). Automatic Bayesian curve fitting, J. R. Statist. Soc., B, 60, 333–350
[3]EuBank, R.L. (1988). Smoothing Splines and Non-parametric Regression, Marcel Dekker, New Yorkand Base
[4]Hoerl, A. E. and Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal proBlems. Technometrics 12, 55-67.
[5]I. J. SchoenBerg, On trigonometric spline interpolation, J. Math. Mech. 13(1964), 795-825
[6]Michael R. OsBorne, Brett Presnell, and Berwin A. Turlach. Knot selection for regression splines via the LASSO. In Computing Science and Statistics. Dimen-sion Reduction, Computational Complexity and Information. Proceedings of the 30th Symposium on the Interface, pages 44–49, 1998
[7]WahBa, G. (1990) Spline Models for OBservational Data.
[8]R. TiBshirani. Regression shrinkage and selection via the LASSO. Journal of the RoyalStatistical Society (Series B), 58:267–288, 1996.
[9]Schumaker, L. L. (1981) Spline functions, Wiley, New York.
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