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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/152776


    Title: 基於B-spline的密度函數估計之節點選取之準則
    Knot selection criteria for density function estimation based on B-spline
    Authors: 江瑞濬
    Chiang, Jui-Chun
    Contributors: 黃子銘
    Huang, Tzee-Ming
    江瑞濬
    Chiang, Jui-Chun
    Keywords: 密度函數估計
    樣條函數近似
    節點選取
    交叉驗證
    Density estimation
    Spline approximation
    Knot selection
    Cross validation
    Date: 2024
    Issue Date: 2024-08-05 13:59:28 (UTC+8)
    Abstract: 本論文在B-spline的背景下進行密度估計，藉由類似帶寬選擇(bandwidth selection)的概念並提出一種挑選節點位置的準則，以估計出較平滑的機率密度函數。節點選取之準則主要透過「抽樣的留一最小平方交叉驗證」(sample leave-one-out least square cross validation) 挑選兩個調節參數並進行估計。通過本文分析不同模擬資料下的結果顯示，此挑選節點位置的準則在估計機率密度函數部分表現良好，因為平均下來的「積分均方誤差」(Integrated Squared Error)數值較小。
    In this thesis, the problem of density estimation based on spline approximation is considered. A procedure for determining knot positions is proposed. The procedure involve two tunning parameters which are determined using sample leave-one-out cross validation. The simulation results indicate that the knot selection procedure performs well since the averages of integrated squared errors are small.
    Reference: [1] Bowman,A.W.(1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71, 353-360.

    [2] C.D.Boor.(1978). A partical guide to splines. Springer New York.

    [3] D.Ruppert.(2002). Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics, 11(4), 735-757

    [4] E.Halpern.(1973). Bayesian spline regression when the number of knots is unknown. Journal of the Royal Statistical Society, B, 35, 347-360.

    [5] E.Parzen.(1962). On estimation of a probability density function and mode. Ann. Math. Statist. , 33(3), 1065-1076

    [6] Hongmei Kang, Falai Chen, Yusheng Li, Jiansong Deng, and Zhouwang Yang. (2015). Knot calculation for spline fitting via sparse optimization. Computer-Aided Design, 58, 179–188.

    [7] I.J.Schoenbreg.(1983). Contributions to the problem of approximation of equidistant data by analytic functions. Quart.~Appl.~Math., 112-144

    [8] J.S.Horne and E.O.Garton.(2006). Likelihood cross-validation versus least squares cross-validation for choosing the smoothing parameter in kernel home-range analysis. The Journal of Wildlife Management, 70, 641–648.

    [9] L.Piegl and W.Tiller.(1996). The NURBS Book. Springer, 81-116

    [10] M.Stone.(1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society , 36(2), 111-147.

    [11] M.P.Wand and M.C.Jones.(1995). Kernel Smoothing. Chapman and Hall.

    [12] Nicolas Molinari, Jean-François Durand, and Robert Sabatier.(2004). Bounded optimal knots for regression splines. Computational statistics and data analysis, 45(2), 159–178.

    [13] Paul, H.E. and Brian, D.M.(1996). Flexible smoothing with b-splines and penalties. Statistical science, 89–102.

    [14] Peter Hall and Huang,Li-Shan.(2001). Nonparametric kernel regression subject to monotonicity constraints. Ann. Statist, 29(3), 624-647.

    [15] Randall,L.E.(1988). Spline smoothing and nonparametric regression. Marcel Dekker.

    [16] Seymour, Geisser.(1975). The predictive sample reuse method with applications. Journal of the American Statistical Association, 70(350), 320-328.

    [17] Silverman,B.W.(1986). Density estimation for statistics and data analysis.
    Chapman and Hall, London, United Kingdom.
    Description: 碩士
    國立政治大學
    統計學系
    111354011
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0111354011
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

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