| dc.contributor.advisor | 黃子銘 | zh_TW |
| dc.contributor.advisor | Huang, Tzee-Ming | en_US |
| dc.contributor.author (Authors) | 賴昱豪 | zh_TW |
| dc.contributor.author (Authors) | Lai, Yu-Hao | en_US |
| dc.creator (作者) | 賴昱豪 | zh_TW |
| dc.creator (作者) | Lai, Yu-Hao | en_US |
| dc.date (日期) | 2023 | en_US |
| dc.date.accessioned | 1-Sep-2023 14:57:01 (UTC+8) | - |
| dc.date.available | 1-Sep-2023 14:57:01 (UTC+8) | - |
| dc.date.issued (上傳時間) | 1-Sep-2023 14:57:01 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0110354018 | en_US |
| dc.identifier.uri (URI) | https://ah.lib.nccu.edu.tw/item?item_id=166377 | - |
| 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) | 110354018 | zh_TW |
| dc.description.abstract (摘要) | 本文主要探討可加性模型的適合度，由於一般無母數迴歸模型會\n有參數過多，估計難度較高，模型結構複雜等等狀況，同時也會有計\n算難度以及效能上的問題，因此，能否使用更簡便的模型同時達到\n估計效果，是我們需要討論的問題，用以評估能否使用可加性模型\n進行資料分析，在評估的過程當中，我們使用到 B-spline 以及 Kernel\nregression 這兩種函數估計的技術，將可加性模型與一般化的模型進\n行對比，並配合 Bootstrap 方法，達到統計檢定的目的。在模擬實驗當\n中，我們使用資料集，實際進行一連串的檢定流程，並且計算檢定的\n型一錯誤率，用以實證此方法的正確性。 | zh_TW |
| dc.description.abstract (摘要) | In this thesis, a goodness-of-fit test for additive models is proposed. Since a\ngeneral non-parametric regression model may have many parameters, parameter estimation can be difficult, and there can be computational challenges and performance\nissues. Therefore, it is of interest to know whether it is possible to use a simpler model\nto fit the data. The feasibility of using the additive model to fit the data is evaluated\nby using the proposed test. In the evaluation, two function estimation techniques are\nemployed, spline approximation, and kernel regression, to compare the fitted results\nbased on the additive model and general model and construct the proposed test. The\np-value of the test is obtained using the Bootstrap method.\nIn the simulation experiments, the proposed test is compared with a test proposed\nby Hardle and Mammen (1993). Based on the simulation results, the proposed test\nhas a better Type I error rate. | en_US |
| dc.description.tableofcontents | 第一章 緒論與背景介紹 1\n第一節 檢定問題 2\n第二節 樣條函數(spline function) 3\n第三節 核迴歸(kernel regression) 5\n第二章 研究方法 7\n第一節 模型估計 7\n第二節 適合度檢定流程 12\n第三節 其他的適合度檢定 15\n第三章 模擬實驗 17\n第一節 適合度檢定 17\n第二節 檢定方法比較 24\n第四章 結論與建議 27\n參考文獻 28 | zh_TW |
| dc.format.extent | 1020958 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0110354018 | en_US |
| dc.subject (關鍵詞) | 適合度檢定 | zh_TW |
| dc.subject (關鍵詞) | 樣條函數 | zh_TW |
| dc.subject (關鍵詞) | 核迴歸 | zh_TW |
| dc.subject (關鍵詞) | 無母數 | zh_TW |
| dc.subject (關鍵詞) | 可加性模型 | zh_TW |
| dc.subject (關鍵詞) | goodness-of-fit test | en_US |
| dc.subject (關鍵詞) | spline approximation | en_US |
| dc.subject (關鍵詞) | kernel regression | en_US |
| dc.subject (關鍵詞) | non-parametric regression | en_US |
| dc.subject (關鍵詞) | additive model | en_US |
| dc.title (題名) | 樣條函數估計下的可加性模型適合度檢定 | zh_TW |
| dc.title (題名) | Goodness-of-Fit Test of Additive Model under Spline | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | Buja, A., Hastie, T., and Tibshirani, R. (1989). Linear smoothers and additive models.\nThe Annals of Statistics, pages 453–510.\nDe Boor, C. (1972). On calculating with b-splines. Journal of Approximation theory,\n6(1):50–62.\nde Jong, P. (1987). A central limit theorem for generalized quadratic forms. Probability\nTheory and Related Fields, 75(2):261–277.\nFan, J., Guo, S., and Hao, N. (2012). Variance estimation using refitted cross-validation\nin ultrahigh dimensional regression. Journal of the Royal Statistical Society: Series B\n(Statistical Methodology), 74(1):37–65.\nFan, J. and Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature\nspace. Journal of the Royal Statistical Society: Series B (Statistical Methodology),\n70(5):849–911.\nGonzález-Manteiga, W. and Crujeiras, R. M. (2013). An updated review of goodness-offit tests for regression models. Test, 22:361–411.\nHardle, W. and Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. The Annals of Statistics, pages 1926–1947.\nNadaraya, E. A. (1964). On estimating regression. Theory of Probability & Its Applications, 9(1):141–142.\nSchoenberg, I. J. (1946). Contributions to the problem of approximation of equidistant data\nby analytic functions. part b. on the problem of osculatory interpolation. a second class\nof analytic approximation formulae. Quarterly of Applied Mathematics, 4(2):112–141.\nWatson, G. S. (1964). Smooth regression analysis. Sankhyā: The Indian Journal of\nStatistics, Series A, 26(4):359–372 | zh_TW |
