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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/67860
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dc.contributor.advisor黃子銘zh_TW
dc.contributor.advisorHuang, Tzee Mingen_US
dc.contributor.author陳柏錞zh_TW
dc.creator陳柏錞zh_TW
dc.date2013en_US
dc.date.accessioned2014-07-29T08:03:19Z-
dc.date.available2014-07-29T08:03:19Z-
dc.date.issued2014-07-29T08:03:19Z-
dc.identifierG0101354028en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/67860-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description統計研究所zh_TW
dc.description101354028zh_TW
dc.description102zh_TW
dc.description.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。zh_TW
dc.description.abstractIn 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.en_US
dc.description.tableofcontents第一章 緒論 1\n第二章 文獻回顧 3\n\n2.1 基於BIC的節點估計方式 3\n\n2.2 APLS 法 6\n\n第三章 研究方法 9\n\n3.1 GAPLS法 9\n\n3.2 實際模擬 11\n\n第四章 模擬與比較 13\n4.1 模擬 c1 ,c2 13\n\n4.2 GAPLS法 與BIC法的比較 16\n\n第五章 結論與建議 27\n5.1 結論 27\n\n5.2 建議 27\n\n5.3 延伸題目 27zh_TW
dc.format.extent1200204 bytes-
dc.format.mimetypeapplication/pdf-
dc.language.isoen_US-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0101354028en_US
dc.subjectB-Splinezh_TW
dc.subjectBICzh_TW
dc.subject無母數方法zh_TW
dc.subject分段多項式zh_TW
dc.subject節點選取zh_TW
dc.subjectB-splineen_US
dc.subjectgeneralized adaptive penalized least squaresen_US
dc.subjectBICen_US
dc.subjectnonparametric　methoden_US
dc.subjectpiecewise polynomialen_US
dc.subjectknot selectionen_US
dc.titleGeneral Adaptive Penalized Least Squares 模型選取方法之模擬與其他方法之比較zh_TW
dc.titleThe Simulation of Model Selection Method for General Adaptive Penalized Least Squares and Comparison with Other Methodsen_US
dc.typethesisen
dc.relation.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.\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.zh_TW
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item.openairecristypehttp://purl.org/coar/resource_type/c_46ec-
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item.grantfulltextopen-
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