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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/32560
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32560


    Title: 廣義壓縮最小平方估計在主成份迴歸上的應用
    Authors: 莫文博
    Contributors: 宋傳欽
    莫文博
    Keywords: 主成份迴歸
    共線性
    廣義壓縮最小平方估計
    後退刪除法
    Date: 2003
    Issue Date: 2009-09-17 13:45:04 (UTC+8)
    Abstract: Mansfield,Webster, and Gunst(1977)提出了結合主成份迴歸及類似於後退刪除法(backward elimination)的變數刪除理論,藉以減輕共線性對建立迴歸模型時所造成的影響。但該變數刪除理論無法有效控制係數估計的變異,使得係數估計的精確度大打折扣。
    本文將王力群(1990)廣義壓縮最小平方估計(generalized shrunken least squares estimator)的概念和Mansfield et al.(1977)變數刪除的理論整合起來,提出了一個刪除變數的修正法。該修正法在變數刪除上的表現雖較為穩健保守,但卻能減輕共線性所造成的影響,並有效壓縮係數估計的變異。
    Reference: 英文部份
    1.Mason, Gunst and Webster [1975], “Regression analysis and problems of multi- collinearity,” Commun. Stat., 4(3),277-292.
    2.Mansfield ,Webster and Gunst [1977], “An analytic variable selection technique for principal component regression” Appl Stat.,26(1),34-40.
    3.Jeffers [1967], ”Two case studies in the application of principal component ana-lysis” Appl Stat.,16,225-236.
    4.Hoerl and Kennard [1970], ”Ridge regression applications to nonorthogonal problems”Technometrics.,12(1),69-82.
    5.G. A. F. Seaber [1976], Linear Regression Analysis, Wiley, New York.
    6.Douglas C, Montgomery Elizabeth A, Peck C Ceoffery Vining [2001], Introduction to Linear Regression Analysis ,3rd ed., Wiley, New York.
    7.John O. Rawlings, Sastry G. Pantula, David A. Dickey [1998], Applied Regression Analysis – A Research Tool ,2nd ed., Springer, New York.
    8.Richard A. Johnson, Dean W. Wichern [1998], Applied Multivariate Statistical Analysis, Prentice Hall.
    中文部份
    1.王力群 [1990],"廣義壓縮最小二乘估計”, 應用概率統計,6卷3期, p219-231。
    2.岳榮先 [1991], “有偏估計的影響分析”, 中國統計學報, 29卷2期。
    3.吳宗正 [1997], “迴歸分析-理論與應用”,復文書局。
    4.鄭錦聰 [2002], “MATLAB程式設計-基礎篇(修訂版)”,全華科技。
    Description: 碩士
    國立政治大學
    應用數學研究所
    89751015
    92
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0089751015
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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