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    題名: 使用彈性網於迴歸樣條的節點選取
    An elastic net based knot selection method for regression spline estimation
    作者: 高崇傑
    Gao, Chong-Jie
    貢獻者: 黃子銘
    高崇傑
    Gao, Chong-Jie
    關鍵詞: 樣條函數
    彈性網
    節點選取
    Spline function
    Elastic net
    Knot selection
    日期: 2018
    上傳時間: 2018-08-01 16:15:31 (UTC+8)
    摘要: 樣條函數是一種用來近似實際函數的方法之一，若我們想使用樣條函數來近似實際的函數時，選擇適當的節點位置會有較好的配適結果。本篇研究模擬在不同的函數曲線以及參數設置下，藉由設置大量的等距節點下，使用彈性網、LASSO、UNIF法，藉由此三種變數選取的方法選取節點，進一步比較對應的樣條函數的估計效果，最終探討三種篩選節點的方法之適用情況。經由模擬，我們發現彈性網的配適結果在實際函數為較平滑曲線時，效果相對三者中是較好的，而在實際函數為較大變化曲線時，UNIF的配適結果是三種方法中較好的。
    Spline functions are often used to approximate smooth functions. In nonparametric regression, if we use a spline function to approximate the regression function, selecting appropriate knots for the spline function will yield better fitting results. In this study, I consider three methods for knot selection: elastic net, LASSO and the UNIF method in [5]. Simulation experiments have been carried out to compare the performance of the three methods. From the simulation results, we have found that when the true regression function is smooth, knot selection base on elastic net gives better results. When the true regression function has large variation, knot selection base on the UNIF method gives better results.
    參考文獻: [1] David Ruppert, M.P. Wand, R.J. Carroll , Semiparametric Regression, Cambridge , 62-72, (2003).
    [2] Arthur E. Hoerl and Robert W. Kennard, Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, Vol. 12, 55-67, (1970).
    [3] Robert Tibshirani, Regression shrinkage and selection via the LASSO, Journal of the RoyalStatistical Society (Series B), 58, 267-288, (1996).
    [4] Hui Zou and Trevor Hastie, Regularization and variable selection via the elastic net, Journal of the RoyalStatistical Society (Series B), 67, 301-320, (2005).
    [5] Xuming He, Lixin Shen, Zuowei Shen, A data-adaptive knot selection scheme for fitting splines, IEEE Signal Processing Letters, Vol.8, 5, 137-139, (2001).
    [6] Larry L. Schumaker, Spline Functions:Basic Theory , third edition, Cambridge, (2007).
    [7] Carl de Boor, A practical guide to splines , Springer, Berlin, (2001).
    [8]Shanggang Zhou and Xiaotong Shen, Adaptive Regression Splines and Accurate Knot Selection Schemes, Journal of the American Statistical Association, Vol. 96, 247-259, (2001).
    描述: 碩士
    國立政治大學
    統計學系
    105354021
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0105354021
    資料類型: thesis
    DOI: 10.6814/THE.NCCU.STAT.012.2018.B03
    顯示於類別:[統計學系] 學位論文

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