| dc.contributor.advisor | 黃子銘 | zh_TW |
| dc.contributor.author (作者) | 高崇傑 | zh_TW |
| dc.contributor.author (作者) | Gao, Chong-Jie | en_US |
| dc.creator (作者) | 高崇傑 | zh_TW |
| dc.creator (作者) | Gao, Chong-Jie | en_US |
| dc.date (日期) | 2018 | en_US |
| dc.date.accessioned | 1-八月-2018 16:15:31 (UTC+8) | - |
| dc.date.available | 1-八月-2018 16:15:31 (UTC+8) | - |
| dc.date.issued (上傳時間) | 1-八月-2018 16:15:31 (UTC+8) | - |
| dc.identifier (其他 識別碼) | G0105354021 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/119129 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 統計學系 | zh_TW |
| dc.description (描述) | 105354021 | zh_TW |
| dc.description.abstract (摘要) | 樣條函數是一種用來近似實際函數的方法之一，若我們想使用樣條函數來近似實際的函數時，選擇適當的節點位置會有較好的配適結果。本篇研究模擬在不同的函數曲線以及參數設置下，藉由設置大量的等距節點下，使用彈性網、LASSO、UNIF法，藉由此三種變數選取的方法選取節點，進一步比較對應的樣條函數的估計效果，最終探討三種篩選節點的方法之適用情況。經由模擬，我們發現彈性網的配適結果在實際函數為較平滑曲線時，效果相對三者中是較好的，而在實際函數為較大變化曲線時，UNIF的配適結果是三種方法中較好的。 | zh_TW |
| dc.description.abstract (摘要) | Spline functions are often used to approximate smooth functions. In nonparametric regression, if we use a spline function to approximate the regression function, selecting appropriate knots for the spline function will yield better fitting results. In this study, I consider three methods for knot selection: elastic net, LASSO and the UNIF method in [5]. Simulation experiments have been carried out to compare the performance of the three methods. From the simulation results, we have found that when the true regression function is smooth, knot selection base on elastic net gives better results. When the true regression function has large variation, knot selection base on the UNIF method gives better results. | en_US |
| dc.description.tableofcontents | 第一章 緒論 1 第二章 文獻回顧 3 2.1 樣條函數相關之文獻回顧 3 2.2 LASSO相關之文獻回顧 3 2.3 elastic net相關之文獻回顧 6 第三章 研究過程 7 3.1 建立Splines迴歸模型以及「節點與變數關係」 7 3.2 基於LASSO、彈性網之節點選取 8 第四章 模擬實驗及結果 12 4.1 模擬實驗步驟與參數設置 12 4.2 改善LASSO、彈性網挑選重要節點產生之問題 14 4.3 實驗結果 15 第五章 結論與建議 20 附錄 21 附錄一 模擬之實際函數圖形 21 附錄二 模擬實驗於各種參數設置下之配適評估指標 25 參考文獻 29 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0105354021 | en_US |
| dc.subject (關鍵詞) | 樣條函數 | zh_TW |
| dc.subject (關鍵詞) | 彈性網 | zh_TW |
| dc.subject (關鍵詞) | 節點選取 | zh_TW |
| dc.subject (關鍵詞) | Spline function | en_US |
| dc.subject (關鍵詞) | Elastic net | en_US |
| dc.subject (關鍵詞) | Knot selection | en_US |
| dc.title (題名) | 使用彈性網於迴歸樣條的節點選取 | zh_TW |
| dc.title (題名) | An elastic net based knot selection method for regression spline estimation | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] David Ruppert, M.P. Wand, R.J. Carroll , Semiparametric Regression, Cambridge , 62-72, (2003). [2] Arthur E. Hoerl and Robert W. Kennard, Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, Vol. 12, 55-67, (1970). [3] Robert Tibshirani, Regression shrinkage and selection via the LASSO, Journal of the RoyalStatistical Society (Series B), 58, 267-288, (1996). [4] Hui Zou and Trevor Hastie, Regularization and variable selection via the elastic net, Journal of the RoyalStatistical Society (Series B), 67, 301-320, (2005). [5] Xuming He, Lixin Shen, Zuowei Shen, A data-adaptive knot selection scheme for fitting splines, IEEE Signal Processing Letters, Vol.8, 5, 137-139, (2001). [6] Larry L. Schumaker, Spline Functions:Basic Theory , third edition, Cambridge, (2007). [7] Carl de Boor, A practical guide to splines , Springer, Berlin, (2001). [8]Shanggang Zhou and Xiaotong Shen, Adaptive Regression Splines and Accurate Knot Selection Schemes, Journal of the American Statistical Association, Vol. 96, 247-259, (2001). | zh_TW |
| dc.identifier.doi (DOI) | 10.6814/THE.NCCU.STAT.012.2018.B03 | - |
