政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/149018

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/149018

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | 全文筆數/總筆數 : 114014/145046 (79%)
造訪人次 : 52050123 線上人數 : 454

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

搜尋範圍

查詢小技巧：

您可在西文檢索詞彙前後加上"雙引號"，以獲取較精準的檢索結果

若欲以作者姓名搜尋，建議至進階搜尋限定作者欄位，可獲得較完整資料

進階搜尋

主頁 ‧ 登入 ‧ 上傳 ‧ 說明 ‧ 關於政大典藏 ‧ 管理

到手機版

政大機構典藏 > 商學院 > 統計學系 > 學位論文 > Item 140.119/149018

請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/149018

題名:	無母數可加性迴歸模型下的變數選取方法之比較 A Comparative Study of Variable Selection Methods in Nonparametric Additive Regression Models
作者:	楊侑 Yang, You
貢獻者:	黃子銘劉惠美 Huang, Tzee-Ming Liu, Hui-Mei 楊侑 Yang, You
關鍵詞:	無母數可加性迴歸模型 B樣條基底樣條函數變數選取 Nonparametric additive regression model B-spline basis Spline function Variable selection
日期:	2023
上傳時間:	2024-01-02 15:17:32 (UTC+8)
摘要:	本論文深入探討了無母數可加性迴歸模型下的變數選取方法。我們採用了由 B 樣條基底組成的樣條函數建立模型，並比較了三種不同的變數選取方法：Group Lasso、Adaptive Group Lasso 和 Group Lasso 結合向前選取法。透過四個不同的指標來評估這些變數選取方法的有效性，同時透過圖表呈現的方式，深入研究變數選取對於樣條函數估計的影響。模擬實驗的結果顯示，在變數選擇的準確度方面，Group Lasso 方法表現較低，但在保留非零函數方面表現優異。相較之下，Adaptive Group Lasso 方法在準確度上優於 Group Lasso 方法，但在保留非零函數方面略遜。根據模擬實驗，我們認為 Adaptive Group Lasso 對懲罰參數的敏感性是造成變數選取效果不理想的原因。未來的研究方向可以致力於優化懲罰參數選擇演算法，以提升 Adaptive Group Lasso 方法的性能。最後，Group Lasso 結合向前選取法的方法在所有指標上表現出色，因此，我們建議將其作為無母數可加性迴歸模型下的首選變數選取方法。同時，模擬實驗結果顯示，當模型選擇剛好的變數時，樣條函數估計效果最佳，進一步突顯了變數選取對於模型函數估計的重要性。 This paper delves into variable selection methods under nonparametric additive regression models. We employed spline functions composed of B-spline basis to construct the model, comparing three different variable selection methods: Group Lasso, Adaptive Group Lasso, and Group Lasso combined with forward selection. The effectiveness of these variable selection methods was evaluated through four distinct metrics, and their impact on spline function estimation was thoroughly investigated through graphical representations. Simulation results indicate that, in terms of variable selection accuracy, Group Lasso performs relatively lower but excels in retaining non-zero functions. In comparison, Adaptive Group Lasso outperforms Group Lasso in accuracy but slightly lags behind in retaining non-zero functions. Based on the simulation experiments, we attribute the suboptimal variable selection performance of Adaptive Group Lasso to its sensitivity to penalty parameters. Future research directions could focus on optimizing penalty parameter selection algorithms to enhance the performance of Adaptive Group Lasso. Finally, the method of combining Group Lasso with forward selection demonstrates outstanding performance across all indicators. We recommend it as the preferred variable selection method under nonparametric additive regression models. Additionally, simulation results highlight that when the model selects precisely the right variables, the spline function estimation achieves optimal results, emphasizing the importance of variable selection in model function estimation.
參考文獻:	De Boor, C. (1972). On calculating with B-splines. Journal of Approximation theory, 6(1):50–62. Efroymson, M. A. (1960). Multiple regression analysis. Mathematical methods for digital computers, 191–203. Fox, J. (2002). Nonparametric regression. Appendix to: An R and S-PLUS Companion to Applied Regression, 1–7. Huang, J., Horowitz, J. L., and Wei, F. (2010). Variable selection in nonparametric additive models. The Annals of Statistics, 38(4):2282–2313. Schoenberg, I. J. (1946). Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae. Quarterly of Applied Mathematics, 4(2):112–141. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 461–464. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1):267–288. Yuan, M. and Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(1):49–67. Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American statistical association, 101(476):1418–1429.
描述:	碩士國立政治大學統計學系 110354021
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0110354021
資料類型:	thesis
顯示於類別:	[統計學系] 學位論文

文件中的檔案:

檔案	描述	大小	格式	瀏覽次數
402101.pdf		908Kb	Adobe PDF	1	檢視/開啟

在政大典藏中所有的資料項目都受到原著作權保護.

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

DSpace Software Copyright © 2002-2004 MIT & Hewlett-Packard / Enhanced by NTU Library IR team Copyright © - 回饋