English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 109952/140891 (78%)
Visitors : 46233066      Online Users : 1130
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
    •  Adv. Search
    Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer Goto mobile version
    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/67860


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/67860


    Title: General Adaptive Penalized Least Squares 模型選取方法之模擬與其他方法之比較
    The Simulation of Model Selection Method for General Adaptive Penalized Least Squares and Comparison with Other Methods
    Authors: 陳柏錞
    Contributors: 黃子銘
    Huang, Tzee Ming
    陳柏錞
    Keywords: B-Spline
    BIC
    無母數方法
    分段多項式
    節點選取
    B-spline
    generalized adaptive penalized least squares
    BIC
    nonparametric　method
    piecewise polynomial
    knot selection
    Date: 2013
    Issue Date: 2014-07-29 16:03:19 (UTC+8)
    Abstract: 在迴歸分析中，若變數間具有非線性 (nonlinear) 的關係時，B-Spline線性迴歸是以無母數的方式建立模型。B-Spline函數為具有節點(knots)的分段多項式，選取合適節點的位置對B-Spline函數的估計有重要的影響，在希望得到B-Spline較好的估計量的同時，我們也想要只用少數的節點就達成想要的成效，於是Huang (2013) 提出了一種選擇節點的方式APLS (Adaptive penalized least squares)，在本文中，我們以此方法進行一些更一般化的設定，並在不同的設定之下，判斷是否有較好的估計效果，且已修正後的方法與基於BIC (Bayesian information criterion)的節點估計方式進行比較，在本文中我們將一般化設定的APLS法稱為GAPLS，並且經由模擬結果我們發現此兩種以B-Spline進行迴歸函數近似的方法其近似效果都很不錯，只是節點的個數略有不同，所以若是對節點選取的個數有嚴格要求要取較少的節點的話，我們建議使用基於BIC的節點估計方式，除此之外GAPLS法也是不錯的選擇。
    In regression analysis, if the relationship between the response variable and the explanatory variables is nonlinear, B-splines can be used to model the nonlinear relationship. Knot selection is crucial in B-spline regression. Huang (2013) propose a method for adaptive estimation, where knots are selected based on penalized least squares. This method is abbreviated as APLS (adaptive penalized least squares) in this thesis. In this thesis, a more general version of APLS is proposed, which is abbreviated as GAPLS (generalized APLS). Simulation studies are carried out to compare the estimation performance between GAPLS and a knot selection method based on BIC (Bayesian information criterion). The simulation results show that both methods perform well and fewer knots are selected using the BIC approach than using GAPLS.
    Reference: [1] Tzee-Ming Huang . An adaptive knot selection method for regression splines via penalized minimum contrast estimation. National ChengChi University. Department. of Statistics. 2013.

    [2] Huang, Tzee-Ming. "Convergence rates for posterior distributions and adaptive
    estimation." The Annals of Statistics 32.4 (2004): 1556-1593.

    [3] Hardle, Wolfgang. Applied nonparametric regression. Vol. 27. Cambridge:
    Cambridge university press, 1990.

    [4] Eubank, Randall L. Nonparametric regression and spline smoothing. CRC press,
    1999.

    [5] 何昕燁，一種基於 BIC 的 B-Spline 節點估計方式. 2012.

    [6] T.A. Springer ，〈線性代數群〉 張瑞吉譯，1987.
    Description: 碩士
    國立政治大學
    統計研究所
    101354028
    102
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0101354028
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

    Files in This Item:

    File SizeFormat
    402801.pdf1172KbAdobe PDF2680View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    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 ©   - Feedback