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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/67860
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/67860


    Title: General Adaptive Penalized Least Squares 模型選取方法之模擬與其他方法之比較
    The Simulation of Model Selection Method for General Adaptive Penalized Least Squares and Comparison with Other Methods
    Authors: 陳柏錞
    Contributors: 黃子銘
    Huang, Tzee Ming
    陳柏錞
    Keywords: B-Spline
    BIC
    無母數方法
    分段多項式
    節點選取
    B-spline
    generalized adaptive penalized least squares
    BIC
    nonparametric method
    piecewise polynomial
    knot selection
    Date: 2013
    Issue Date: 2014-07-29 16:03:19 (UTC+8)
    Abstract: 在迴歸分析中,若變數間具有非線性 (nonlinear) 的關係時,B-Spline線性迴歸是以無母數的方式建立模型。B-Spline函數為具有節點(knots)的分段多項式,選取合適節點的位置對B-Spline函數的估計有重要的影響,在希望得到B-Spline較好的估計量的同時,我們也想要只用少數的節點就達成想要的成效,於是Huang (2013) 提出了一種選擇節點的方式APLS (Adaptive penalized least squares),在本文中,我們以此方法進行一些更一般化的設定,並在不同的設定之下,判斷是否有較好的估計效果,且已修正後的方法與基於BIC (Bayesian information criterion)的節點估計方式進行比較,在本文中我們將一般化設定的APLS法稱為GAPLS,並且經由模擬結果我們發現此兩種以B-Spline進行迴歸函數近似的方法其近似效果都很不錯,只是節點的個數略有不同,所以若是對節點選取的個數有嚴格要求要取較少的節點的話,我們建議使用基於BIC的節點估計方式,除此之外GAPLS法也是不錯的選擇。
    In regression analysis, if the relationship between the response variable and the explanatory variables is nonlinear, B-splines can be used to model the nonlinear relationship. Knot selection is crucial in B-spline regression. Huang (2013) propose a method for adaptive estimation, where knots are selected based on penalized least squares. This method is abbreviated as APLS (adaptive penalized least squares) in this thesis. In this thesis, a more general version of APLS is proposed, which is abbreviated as GAPLS (generalized APLS). Simulation studies are carried out to compare the estimation performance between GAPLS and a knot selection method based on BIC (Bayesian information criterion). The simulation results show that both methods perform well and fewer knots are selected using the BIC approach than using GAPLS.
    Reference: [1] Tzee-Ming Huang . An adaptive knot selection method for regression splines via penalized minimum contrast estimation. National ChengChi University. Department. of Statistics. 2013.

    [2] Huang, Tzee-Ming. "Convergence rates for posterior distributions and adaptive
    estimation." The Annals of Statistics 32.4 (2004): 1556-1593.

    [3] Hardle, Wolfgang. Applied nonparametric regression. Vol. 27. Cambridge:
    Cambridge university press, 1990.

    [4] Eubank, Randall L. Nonparametric regression and spline smoothing. CRC press,
    1999.

    [5] 何昕燁,一種基於 BIC 的 B-Spline 節點估計方式. 2012.

    [6] T.A. Springer ,〈線性代數群〉 張瑞吉譯,1987.
    Description: 碩士
    國立政治大學
    統計研究所
    101354028
    102
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0101354028
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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