| dc.contributor.advisor | 黃子銘 | zh_TW |
| dc.contributor.author (Authors) | 林哲宇 | zh_TW |
| dc.contributor.author (Authors) | Lin, Zhe-Yu | en_US |
| dc.creator (作者) | 林哲宇 | zh_TW |
| dc.creator (作者) | Lin, Zhe-Yu | en_US |
| dc.date (日期) | 2020 | en_US |
| dc.date.accessioned | 5-May-2020 11:56:46 (UTC+8) | - |
| dc.date.available | 5-May-2020 11:56:46 (UTC+8) | - |
| dc.date.issued (上傳時間) | 5-May-2020 11:56:46 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0106354016 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/129647 | - |
| 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) | 106354016 | zh_TW |
| dc.description.abstract (摘要) | 本研究是根據Yuan[12]提出的Multi-resolution B-spline basis節點放置方法對於節點的篩選做進一步的改良，以擾動項ε的變異數σ^2為標準，採用向後刪除的概念提出方法一及方法二，也將其改良後的方法透過張量積擴展到二維曲面的估計，以copula密度函數作為迴歸函數，與核迴歸中的局部線性迴歸的結果進行比較。 依模擬結果，方法一會因為σ的估計膨脹而篩選掉過多節點，方法二受σ的估計影響較小，估計效果較佳，也較為穩定。 在以copula密度函數作為迴歸函數的模擬實驗中，較不平滑的迴歸函數使用方法二來估計，估計效果較佳；較平滑的迴歸函數使用局部線性迴歸來估計為最佳，但如果在σ的估計上能更好，方法二的估計效果可能優於局部線性迴歸。 | zh_TW |
| dc.description.abstract (摘要) | This thesis is based on the multi-resolution B-spline basis knots placement method proposed by Yuan[12] to further improve the selection of knots. Based on the variation of the disturbance term, Method 1 and Method 2,are proposed using the concept of backward deletion. The improved method is also extended to the estimation of the two-dimensional surface. through the tensor product. Simulation studies have been carried out to compare the performance of Methods 1 and 2, and local linear regression. According to the results of simulation studies, Method 1 tends to filter out too many knots because of the large estimation error of σ,and Method 2 is less affected by the estimation of σ. The estimation based on Method 2 is more accurate and stable. In the studies where Methods 1 and 2, and local linear regression are compared, Method 2 outperforms local linear regression when the regression function is less smooth. When the regression function is smooth, local linear regression performs better than Method 2. However,if the estimation of σ can be better, the estimation accuracy of Method 2 may be better than local linear regression. | en_US |
| dc.description.tableofcontents | 1 緒論 12 文獻探討 23 研究方法 43.1 Multi-resolution B-spline basis 43.2 Lasso 63.3 Cross Validation 63.4 懲罰係數選取 73.5 節點篩選方法 83.5.1 方法一 93.5.2 方法二 93.6 Local Linear Regression 94 模擬資料分析 114.1 模擬函數為(4.1)式g時的實驗結果 124.2 模擬函數為張量積B-spline基底生成時的實驗結果 144.3 方法一、方法二和local linear估計的比較 165 結論與建議 215.1 研究結論 21參考文獻 23附錄一 25附錄二 29 | zh_TW |
| dc.format.extent | 2301832 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0106354016 | en_US |
| dc.subject (關鍵詞) | B-spline迴歸 | zh_TW |
| dc.subject (關鍵詞) | 節點選取 | zh_TW |
| dc.subject (關鍵詞) | 曲面估計 | zh_TW |
| dc.subject (關鍵詞) | B-spline regression | en_US |
| dc.subject (關鍵詞) | Knot selection | en_US |
| dc.subject (關鍵詞) | Surface estimation | en_US |
| dc.title (題名) | 基於 multi-resolution B-spline basis 之二維曲面估計 | zh_TW |
| dc.title (題名) | Estimate of the two-dimensions surface based on multi-resolution B-spline basis | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] William S. Cleveland and Susan J. Devlin. Locally weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association, 83(403):596–610, 1988.[2] WS Cleveland. Lowess: A program for smoothing scatterplots by robust locallyweighted regression. The American Statistician, 35:54, 1981.[3] Jerome H. Friedman. Multivariate adaptive regression splines. Ann. Statist., 19(1):1–67, 1991.[4] David L. B. Jupp. Approximation to data by splines with free knots. SIAM Journal on Numerical Analysis, 15(2):328–343, 1978.[5] Hongmei Kang, Falai Chen, Yusheng Li, Jiansong Deng, and Zhouwang Yang.Knot calculation for spline fitting via sparse optimization. Computer-Aided Design, 58:179–188, 2015.[6] Mary J. Lindstrom. Penalized estimation of free-knot splines. Journal of Computational and Graphical Statistics, 8(2):333–352, 1999.[7] Satoshi Miyata and Xiaotong Shen. Adaptive free-knot splines. Journal of Computational and Graphical Statistics, 12(1):197–213, 2003.[8] M. R. Osborne, B. Presnell, and B. A. Turlach. Knot selection for regression splines via the lasso. In Dimension Reduction, Computational Complexity, and Information, pages 44–49. America, Inc, 1998.[9] Abe Sklar. Fonctions de r´epartition "a n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Universit´e de Paris, 8:229–231, 1959.[10] R. Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society (Series B), 58:267–288, 1996.[11] Wannes Van Loock, Goele Pipeleers, J. Schutter, and Jan Swevers. A convex optimization approach to curve fitting with b-splines. IFAC Proceedings Volumes (IFAC-PapersOnline), 18:2290–2295, 2011.[12] Yuan Yuan, Nan Chen, and Shiyu Zhou. Adaptive b-spline knot selection using multi-resolution basis set. IIE Transactions, 45:1263–1277, 2013.[13] Shanggang Zhou and Xiaotong Shen. Spatially adaptive regression splines and accurate knot selection schemes. Journal of the American Statistical Association, 96(453):247–259, 2001 | zh_TW |
| dc.identifier.doi (DOI) | 10.6814/NCCU202000415 | en_US |
