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    题名: 比較使用Kernel和Spline法的傘型迴歸估計
    Compare the Estimation on Umbrella Function by Using Kernel and Spline Regression Method
    作者: 賴品霖
    Lai, Pin Lin
    贡献者: 黃子銘
    賴品霖
    Lai, Pin Lin
    关键词: 核迴歸
    樣條迴歸
    無母數迴歸
    傘型函數
    Kernel regression
    Spline regression
    Nonparametric regression
    Umbrella function
    日期: 2016
    上传时间: 2016-07-11 16:55:04 (UTC+8)
    摘要: 本研究探討常用的兩個無母數迴歸方法，核迴歸與樣條迴歸，在具有傘型限制式下，對於傘型函數的估計與不具限制式下的傘型函數估計比較，同時也探討不同誤差變異對估計結果的影響，並進一步探討受限制下兩方法的估計比較。本研究採用「估計頂點位置與實際頂點位置差」及「誤差平方和」作為衡量估計結果的指標。在帶寬及節點的選取上，本研究採用逐一剔除交互驗證法來篩選。模擬結果顯示，受限制的核函數在誤差變異較大的頂點位置估計較佳，誤差變異縮小時反而頂點位置估計較差，受限制的B-樣條函數也有類似的狀況。而在兩方法的比較上，對於較小的誤差變異，核函數的頂點位置估計能力不如樣條函數，但在整體的誤差平方和上卻沒有太大劣勢，當誤差變異較大時，核函數的頂點位置估計能力有所提升，整體誤差平方和仍舊維持還不錯的結果。
    In this study, we give an umbrella order constraint on kernel and spline regression model. We compare their estimation in two measurements, one is the difference of estimate peak and true peak, the other one is the sum of square difference on predict and the true value. We use leave-one-out cross validation to select bandwidth for kernel function and also to decide the number of knots for spline function. The effect of different error size is also considered. Some of R packages are used when doing simulation. The result shows that when the error size is bigger, the prediction of peak location is better in both constrained kernel and spline estimation. The constrained spline regression tends to provide better peak location estimation compared to constrained kernel regression.
    參考文獻: 1. Boor, C. D. (1972) “On calculating with B-splines.”, Journal of Approximation theorey, 6, 50-62.
    2. Cressie, N. A. C. and Read, T. R. C. (1984) “Multinomial goodness-of-fit tests.”, J. Roy. Statist. Soc. Ser. B, 46, 440-464
    3. Du, P., Parmeter, C. F. and Racine, J. S. (2013) “Nonparametricc kernel regression with multiple predictors and multiple shape constraints.”, Statistica Sinica, 23, 1347-1371.
    4. Fan, J. (1992) “Design-adaptive nonparametric regression.”, J. Amer. Statist. Assoc., 87, 998-1004.
    5. Gasser, T. and Müller, H.-G. (1979) “Kernel estimation of regression functions.”, In Smoothing Techniques for Curve Estimation, 23(68), Springer-Verlag, New York.
    6. Hall, P. and Haung, L.-S. (2001) “Noparametric kernel regresson subject to monotonicity constraints.”, Ann. Statist, 29(3), 624-647.
    7. He, X., and Shi, P.(1998) “Monotone B-spline smoothing.”, J. Amer. Statist. Assoc., 93(442), 643-650.
    8. Mammen, E. and Thomas-Agnan, C. (1998) “Smoothing splines and shape restrictions.”, Scandinavian Journal of Statistics, 26, 239-252.
    9. Nadaraya, E. A. (1965) “On nonparametric estimates of density functions and regression curves”, Theory Probab. Appl., 10, 186-190.
    10. Priestley, M. B. and Chao, M. T. (1972) “Nonparametric function fitting.”, J. Roy. Statist. Soc. Ser. B, 34, 385-392
    11. Racine, J. and Li, Q. (2004) “Nonparametric estimation of regression functions with both categorical and continuous data.”, J. Econometrics, 119, 99-130.
    12. Schumaker, L. L. (1981) Spline functions, Wiley, New York.
    13. Stone, M. (1974) “Cross-validatory choice and assessment of statistical predictions.”, Roy. Statist. Soc. Ser. B, 36(2), 111-147
    14. Stout, F. (2008) “Unimodal regression via prefix isotonic regression.”, Computational Statistics and Data Analysis, 53, 289-297.
    15. Watson, G. S. (1964) “Smooth regression analysis.”, Sankhya ̅, 26(15), 175-184.
    描述: 碩士
    國立政治大學
    統計學系
    102354008
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G1023540081
    数据类型: thesis
    显示于类别:[統計學系] 學位論文

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