政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32560

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32560

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > 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:	[Department of Mathematical Sciences] Theses

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