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研究生: 蔡侑勳
論文名稱: Fitting Penalized Fourier Regression in Practice
指導教授: 黃禮珊
口試委員: 黃禮珊
徐南蓉
吳漢銘
學位類別: 碩士
Master
系所名稱: 理學院 - 統計學研究所
Institute of Statistics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 138
中文關鍵詞: 無母數傅立葉懲罰R語言
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  • 對於配適處罰傅立葉回歸,吳(2013)提供了一些R-函數的設置單變量非參數回歸,部分線性模型,加性模型和非參數邏輯和泊松回歸。我們完善這些功能遵循的R-函數格式使用者可以應用通用的R-函數總結,summary, plot, lines, fitted, predict, and residuals.。此外,我們寫一些R-函數利用AICc或BIC來選擇懲罰參數。我們用一些數據例子來說明我們的R-函數,而且用一個小的模擬來比較懲罰傅立葉迴歸和PS。


    For tting penalized Fourier regression, Wu (2013) provide some R-functions in the settings of univariate nonparametric regression, partial linear models, additive models, and nonparametric logistic and Poisson regression. We improve these functions to follow the R-function format so that users could apply generic R-functions summary, plot, lines, fitted, predict, and residuals. In addition, we write some R-function to select penalty parameters by AICc or BIC. Some data examples are used to illustrate our R-functions. A small simulation study is conducted to compare the penalized Fourier to spline approaches.

    Contents 1 Introduction 3 2 Background 5 2.1 Penalized Fourier Regression . . . . . . . . . . . . . 5 2.2 Partial Linear Model . . . . . . . . . . . . . . . . . 7 2.3 Logistic and Poisson Regression . . . . . . . . . . . 7 3 R-functions of Smoothing Parameter Selection 9 3.1 R-methods. . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Univariate regression. . . . . . . . . . . . . . . . . 9 3.2.1 Usage of lmm.pf.select . . . . . . . . . . . . . . 10 3.2.2 Usage of qr.pf.select . . . . . . . . . . . . . . . 16 3.3 Partial Linear Models . . . . . . . . . . . . . . . . 24 3.3.1 Usage of lmm.plm.select . . . . . . . . . . . . . . 24 3.3.2 Usage of qr.plm.select. . . . . . . . . . . . . . . 30 3.4 Nonparametric logistic and Poisson regression . . . . 36 3.4.1 Usage of lmm.logistic.select. . . . . . . . . . . . 36 3.4.2 Usage of qr.logistic.select . . . . . . . . . . . .41 3.4.3 Usage of lmm.pois.select . . . . . . . . . . . . . .48 3.4.4 Usage of qr.pois.select . . . . . . . . . . . . . . 52 4 Simulation Study 59 4.1 Penalty form M2 . . . . . . . . . . . . . . . . . . . 60 4.2 Quadratic Penalty form M1 . . . . . . . . . . . . . . 61 5 Discussion 66 Figures 67 Tables 85 Appendix: Code of R-functions 95 References 137

    Akaike, H., (1973). Information theory and an extension of the maximum likelihood principle, 2nd International Symposium on Information Theory, B.N. Petrov and F.Csaki
    (eds.), Akademiai Kiado, Budapest, 267-281.
    
    Berndt, E. R. (1991). The Practice of Econometrics. New York: Addison-Wesley.

    Bowman, A. W., and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analy-sis. London: Oxford.
    
    Eubank, R. L. (1999). Nonparametric Regression and Spline Smoothing. New York: Mar- cel Dekker.
    
    Eubank, R. L., and Speckman, P. (1990). Curve tting by polynomial-trigonometric regression. Biometrika, 77, 1-9.

    Fan, J., and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications. London: Chapman and Hall.
    
    Graybill, F. (1976). Theory and Application of the Linear Model. North Scituate, Duxbury.
    
    Huang, L. S. and Chan, K. S. (2014). Local polynomial and penalized trigonometric series regression. Statistica Sinica, to appear.
    
    Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples. Biometrika, 76, 297-307.
    
    Hurvich, C. M., Jerey, S. S., and Tasi, C. L. (1998). Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion. Journal of
    137 the Royal Statistical Society: Series B (Statistical Methodology),60, 271-293.

    Long, J. S. and Freese, J. (2006). Regression Models for Categorical Dependent Variables Using Stata, Second ed. College -Station, TX: Stata Press.
    
    Ruppert, D., Wand, M. P., and Carroll, R. J. (2003). Semiparametric Regression. London: Cambridge University Press.
    
    Sigrist, M. (Ed.) (1994). Air Monitoring by Spectroscopic Techniques (Chemical Analysis Series, vol. 197). New York: Wiley.
    
    Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics 6: 461-464.
    
    Wang, Y. (2011). Smoothing Splines. Boca Raton: CRC Press.
    
    Wood, S. N. (2006). Genaralized Additive Models: An Introduction with R. Boca Raton: CRC Press

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