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题名: 利用均方誤矩陣於迴歸分析中主成份之選擇
作者: 蔡秒玉;施葦
贡献者: 統計資訊研究所
关键词: 多重共線性;主成份迴歸;均方誤矩陣
Multicollinearity;Principal components regression;Mean square error matrix
日期: 2007-06
上传时间: 2012-10-25T09:03:25Z
出版者: The Chinese Statistical Association
摘要: 當採用主成份迴歸分析來減輕解釋變數間的多重共線性時，傳統上會刪除特徵值較小的主成份，但這些被刪除的主成份中，有一些可能與被解釋變數有較高的相關性。因此，我們探討並比較兩種選取主成份之方式，一為採取以特徵值較大的方式來選取主成份，另一以被解釋變數和主成份有較高之線性相關來選取主成份。本文在複迴歸模式下，利用迴歸係數估計值之均方誤矩陣為準則，將樣本空間分成九個互斥組合，比較上述二種方式所得之主成份迴歸估計值和一般最小平方估計值，以得到其充分必要條件式，並且根據此充要條件，建立交集－聯集檢定，同時推導出檢定統計式為非中心F分配，如此完成了對此兩種主成份迴歸估計值和最小平方估計值的比較準則。其中三種組合可得到唯一最佳的迴歸估計值，另五種組合則可比較出任兩個估計值之優劣。
In the principal components regression, we are used to delete the principal components with small eigenvalues to remedy the multicollinearity problem. But these deleted principal components may have higher correlation with the response variable than the rest. Therefore, we discuss two methods of choosing the principal components, the principal components with higher eigenvalues, and the principal components that have higher correlation with the response variable. In this paper, mean square error matrix of estimators for regression coefficients is used as the criterion to compare the two methods and method of ordinary least squares in the multiple regression models. The necessary and sufficient conditions are obtained and the corresponding tests for verifying the conditions are also derived. Three tests can determine the best regression estimator among the two principal components regression estimators and ordinary least square estimator. The others can obtain a superior estimator between a pair of these three regression estimators.
關聯: 中國統計學報, 45(2): 206-220
显示于类别:[統計資訊研究所] 期刊論文

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