政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/115722
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  全文笔数/总笔数 : 109952/140887 (78%)
造访人次 : 46288209      在线人数 : 757
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
搜寻范围 查询小技巧：
  • 您可在西文检索词汇前后加上"双引号"，以获取较精准的检索结果
  • 若欲以作者姓名搜寻，建议至进阶搜寻限定作者字段，可获得较完整数据
    •  进阶搜寻
    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/115722


    请使用永久网址来引用或连结此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/115722


    题名: 交叉驗證用於迴歸樣條的模型選擇之探討
    作者: 謝式斌
    贡献者: 黃子銘
    謝式斌
    关键词: 交叉驗證
    迴歸樣條
    節點
    模型選擇
    Knots
    Cross validation
    Splines
    日期: 2018
    上传时间: 2018-02-02 10:45:49 (UTC+8)
    摘要: 在無母數的迴歸當中，因為原始的函數類型未知，所以常用已知特定類型的函數來近似未知的函數，而spline函數也可以用來近似未知的函數，但是要估計spline函數就需要設定節點(knots)，越多的節點越能準確近似原始函數的內容，可是如果節點太多有較多的參數要估計, 就會變得比較不準確，所以選擇適合節點個數就變得很重要。
    在本研究中，用交叉驗證的方式來尋找適合的節點個數， 考慮了幾種不同切割資料方式來決定訓練資料和測試資料, 並比較不同切割資料的方式下選擇節點的結果與函數估計的效果。
    In this thesis, I consider the problem of estimating an unknown regression function using spline approximation.
    Splines are piecewise polynomials jointed at knots. When using splines to approximate unknown functions, it is crucial to determine the number of knots and the knot locations. In this thesis, I determine the knot locations using least squares for given a given number of knots, and use cross-validation to find appropriate number of knots. I consider three methods to split the data into training data and testing data, and compare the estimation results.
    參考文獻: David Ruppert, Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics, 11(4):735–757, 2002.

    E.F. Halpern. Bayesian spline regression when the number of knots is unknown. Journal of the Royal Statistical Society B, 35:347–60, 1973.

    Issac Jacob Schoenberg. 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 appoximation formulae. Quart. Appl. Math, 4:112–141, 1983.

    Jeff Racine. Feasible cross-validatory model selection for general stationary processes. Journal of Applied Econometrics, 12(2):169–179, 1997.

    J Shao. Linear model selection by cross-validation. Journal of the American Statistical Association, 88(422):486–95, 1993.

    Meyer Mary C. Inference using shape-restricted regression splines. The Annals of Applied Statistics, 2(3):1013–1033, 2008.

    M Stone. Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, 36:111–147, 1974.

    R Picard, R and D Cook, R. Cross-validation of regression models. Journal of the American Statistical Association, 79:575–583, 1984.

    S Geisser. A predictive sample reuse method with application. Journal of the American Statistical Association, 70:320–8, 1975.
    描述: 碩士
    國立政治大學
    統計學系
    104354028
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0104354028
    数据类型: thesis
    显示于类别:[統計學系] 學位論文

    文件中的档案:

    档案 大小格式浏览次数
    402801.pdf786KbAdobe PDF2272检视/开启


    在政大典藏中所有的数据项都受到原著作权保护.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - 回馈