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https://ah.lib.nccu.edu.tw/handle/140.119/67860
題名: | 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 |
作者: | 陳柏錞 | 貢獻者: | 黃子銘 Huang, Tzee Ming 陳柏錞 |
關鍵詞: | 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 |
日期: | 2013 | 上傳時間: | 29-Jul-2014 | 摘要: | 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. |
參考文獻: | [1] Tzee-Ming Huang . An adaptive knot selection method for regression splines via penalized minimum contrast estimation. National ChengChi University. Department. of Statistics. 2013.\n\n[2] Huang, Tzee-Ming. "Convergence rates for posterior distributions and adaptive \nestimation." The Annals of Statistics 32.4 (2004): 1556-1593.\n\n[3] Hardle, Wolfgang. Applied nonparametric regression. Vol. 27. Cambridge: \nCambridge university press, 1990.\n\n[4] Eubank, Randall L. Nonparametric regression and spline smoothing. CRC press, \n1999.\n\n[5] 何昕燁,一種基於 BIC 的 B-Spline 節點估計方式. 2012.\n\n[6] T.A. Springer ,〈線性代數群〉 張瑞吉譯,1987. | 描述: | 碩士 國立政治大學 統計研究所 101354028 102 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0101354028 | 資料類型: | thesis |
Appears in Collections: | 學位論文 |
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402801.pdf | 1.17 MB | Adobe PDF2 | View/Open |
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