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| Title: | 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 |
| Authors: | 孟耿德
Meng, Geng De |
| Contributors: | 黃子銘
Huang, Tzee Ming
孟耿德
Meng, Geng De |
| Keywords: | 變數選取
最小壓縮法
KNOT
LASSO |
| Date: | 2017 |
| Issue Date: | 2017-09-13 14:12:10 (UTC+8) |
| Abstract: | 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. |
| Reference: | 參考文獻
[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. |
| Description: | 碩士
國立政治大學
統計學系
104354029 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G1043540291 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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