| dc.contributor.advisor | 黃子銘 | zh_TW |
| dc.contributor.advisor | Huang, Tzee Ming | en_US |
| dc.contributor.author (Authors) | 陳柏錞 | zh_TW |
| dc.creator (作者) | 陳柏錞 | zh_TW |
| dc.date (日期) | 2013 | en_US |
| dc.date.accessioned | 29-Jul-2014 16:03:19 (UTC+8) | - |
| dc.date.available | 29-Jul-2014 16:03:19 (UTC+8) | - |
| dc.date.issued (上傳時間) | 29-Jul-2014 16:03:19 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0101354028 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/67860 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 統計研究所 | zh_TW |
| dc.description (描述) | 101354028 | zh_TW |
| dc.description (描述) | 102 | zh_TW |
| dc.description.abstract (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。 | zh_TW |
| dc.description.abstract (摘要) | 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. | en_US |
| dc.description.tableofcontents | 第一章 緒論 1第二章 文獻回顧 32.1 基於BIC的節點估計方式 32.2 APLS 法 6第三章 研究方法 93.1 GAPLS法 93.2 實際模擬 11第四章 模擬與比較 134.1 模擬 c1 ,c2 134.2 GAPLS法 與BIC法的比較 16第五章 結論與建議 275.1 結論 275.2 建議 275.3 延伸題目 27 | zh_TW |
| dc.format.extent | 1200204 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0101354028 | en_US |
| dc.subject (關鍵詞) | B-Spline | zh_TW |
| dc.subject (關鍵詞) | BIC | zh_TW |
| dc.subject (關鍵詞) | 無母數方法 | zh_TW |
| dc.subject (關鍵詞) | 分段多項式 | zh_TW |
| dc.subject (關鍵詞) | 節點選取 | zh_TW |
| dc.subject (關鍵詞) | B-spline | en_US |
| dc.subject (關鍵詞) | generalized adaptive penalized least squares | en_US |
| dc.subject (關鍵詞) | BIC | en_US |
| dc.subject (關鍵詞) | nonparametric method | en_US |
| dc.subject (關鍵詞) | piecewise polynomial | en_US |
| dc.subject (關鍵詞) | knot selection | en_US |
| dc.title (題名) | General Adaptive Penalized Least Squares 模型選取方法之模擬與其他方法之比較 | zh_TW |
| dc.title (題名) | The Simulation of Model Selection Method for General Adaptive Penalized Least Squares and Comparison with Other Methods | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (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.[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. | zh_TW |
