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題名 樣條函數估計下的可加性模型適合度檢定
Goodness-of-Fit Test of Additive Model under Spline
作者 賴昱豪
Lai, Yu-Hao
貢獻者 黃子銘
Huang, Tzee-Ming
賴昱豪
Lai, Yu-Hao
關鍵詞 適合度檢定
樣條函數
核迴歸
無母數
可加性模型
goodness-of-fit test
spline approximation
kernel regression
non-parametric regression
additive model
日期 2023
上傳時間 1-Sep-2023 14:57:01 (UTC+8)
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
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
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
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
進行資料分析，在評估的過程當中，我們使用到 B-spline 以及 Kernel
regression 這兩種函數估計的技術，將可加性模型與一般化的模型進
行對比，並配合 Bootstrap 方法，達到統計檢定的目的。在模擬實驗當
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
型一錯誤率，用以實證此方法的正確性。
In this thesis, a goodness-of-fit test for additive models is proposed. Since a
general non-parametric regression model may have many parameters, parameter estimation can be difficult, and there can be computational challenges and performance
issues. Therefore, it is of interest to know whether it is possible to use a simpler model
to fit the data. The feasibility of using the additive model to fit the data is evaluated
by using the proposed test. In the evaluation, two function estimation techniques are
employed, spline approximation, and kernel regression, to compare the fitted results
based on the additive model and general model and construct the proposed test. The
p-value of the test is obtained using the Bootstrap method.
In the simulation experiments, the proposed test is compared with a test proposed
by Hardle and Mammen (1993). Based on the simulation results, the proposed test
has a better Type I error rate.
參考文獻 Buja, A., Hastie, T., and Tibshirani, R. (1989). Linear smoothers and additive models.
The Annals of Statistics, pages 453–510.
De Boor, C. (1972). On calculating with b-splines. Journal of Approximation theory,
6(1):50–62.
de Jong, P. (1987). A central limit theorem for generalized quadratic forms. Probability
Theory and Related Fields, 75(2):261–277.
Fan, J., Guo, S., and Hao, N. (2012). Variance estimation using refitted cross-validation
in ultrahigh dimensional regression. Journal of the Royal Statistical Society: Series B
(Statistical Methodology), 74(1):37–65.
Fan, J. and Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature
space. Journal of the Royal Statistical Society: Series B (Statistical Methodology),
70(5):849–911.
González-Manteiga, W. and Crujeiras, R. M. (2013). An updated review of goodness-offit tests for regression models. Test, 22:361–411.
Hardle, W. and Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. The Annals of Statistics, pages 1926–1947.
Nadaraya, E. A. (1964). On estimating regression. Theory of Probability & Its Applications, 9(1):141–142.
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.
Watson, G. S. (1964). Smooth regression analysis. Sankhyā: The Indian Journal of
Statistics, Series A, 26(4):359–372
描述 碩士
國立政治大學
統計學系
110354018
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110354018
資料類型 thesis
dc.contributor.advisor 黃子銘zh_TW
dc.contributor.advisor Huang, Tzee-Mingen_US
dc.contributor.author (Authors) 賴昱豪zh_TW
dc.contributor.author (Authors) Lai, Yu-Haoen_US
dc.creator (作者) 賴昱豪zh_TW
dc.creator (作者) Lai, Yu-Haoen_US
dc.date (日期) 2023en_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) G0110354018en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/146903-
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) 110354018zh_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
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
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
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
進行資料分析，在評估的過程當中，我們使用到 B-spline 以及 Kernel
regression 這兩種函數估計的技術，將可加性模型與一般化的模型進
行對比，並配合 Bootstrap 方法，達到統計檢定的目的。在模擬實驗當
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
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
general non-parametric regression model may have many parameters, parameter estimation can be difficult, and there can be computational challenges and performance
issues. Therefore, it is of interest to know whether it is possible to use a simpler model
to fit the data. The feasibility of using the additive model to fit the data is evaluated
by using the proposed test. In the evaluation, two function estimation techniques are
employed, spline approximation, and kernel regression, to compare the fitted results
based on the additive model and general model and construct the proposed test. The
p-value of the test is obtained using the Bootstrap method.
In the simulation experiments, the proposed test is compared with a test proposed
by Hardle and Mammen (1993). Based on the simulation results, the proposed test
has a better Type I error rate.		en_US
dc.description.tableofcontents 第一章 緒論與背景介紹 1
第一節 檢定問題 2
第二節 樣條函數(spline function) 3
第三節 核迴歸(kernel regression) 5
第二章 研究方法 7
第一節 模型估計 7
第二節 適合度檢定流程 12
第三節 其他的適合度檢定 15
第三章 模擬實驗 17
第一節 適合度檢定 17
第二節 檢定方法比較 24
第四章 結論與建議 27
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/#G0110354018en_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 testen_US
dc.subject (關鍵詞) spline approximationen_US
dc.subject (關鍵詞) kernel regressionen_US
dc.subject (關鍵詞) non-parametric regressionen_US
dc.subject (關鍵詞) additive modelen_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 Splineen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Buja, A., Hastie, T., and Tibshirani, R. (1989). Linear smoothers and additive models.
The Annals of Statistics, pages 453–510.
De Boor, C. (1972). On calculating with b-splines. Journal of Approximation theory,
6(1):50–62.
de Jong, P. (1987). A central limit theorem for generalized quadratic forms. Probability
Theory and Related Fields, 75(2):261–277.
Fan, J., Guo, S., and Hao, N. (2012). Variance estimation using refitted cross-validation
in ultrahigh dimensional regression. Journal of the Royal Statistical Society: Series B
(Statistical Methodology), 74(1):37–65.
Fan, J. and Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature
space. Journal of the Royal Statistical Society: Series B (Statistical Methodology),
70(5):849–911.
González-Manteiga, W. and Crujeiras, R. M. (2013). An updated review of goodness-offit tests for regression models. Test, 22:361–411.
Hardle, W. and Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. The Annals of Statistics, pages 1926–1947.
Nadaraya, E. A. (1964). On estimating regression. Theory of Probability & Its Applications, 9(1):141–142.
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.
Watson, G. S. (1964). Smooth regression analysis. Sankhyā: The Indian Journal of
Statistics, Series A, 26(4):359–372		zh_TW