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| Title: | 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 |
| Authors: | 賴昱豪
Lai, Yu-Hao |
| Contributors: | 黃子銘
Huang, Tzee-Ming
賴昱豪
Lai, Yu-Hao |
| Keywords: | 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 |
| Date: | 2023 |
| Issue Date: | 2023-09-01 14:57:01 (UTC+8) |
| Abstract: | 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. |
| Reference: | 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 |
| Description: | 碩士
國立政治大學
統計學系
110354018 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0110354018 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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| 401801.pdf | | 997Kb | Adobe PDF2 | 0 | View/Open |
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