权回归与一般影响度量
A Kind of General Influence Measure on the Linear Weighted Regression
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摘要: 权回归模型是近年来文献中较多涉及的一种.本文从回归诊断的角度进一步研究了它的若干问题.如扰动、影响度量及估计效率等.由于这类模型的一般性,因而本文的结果均可看作回归诊断中较成熟的一些结论的推广.Abstract: The linear weighted regression model is one of the models studied in many articles in recent years. Some further problems, such as disturbation, influence measure and estimate efficiency, have been discussed in this paper on the basis of the regression diagnosties. The partial conclusions of this paper are the extension of the familiar concepts in the regression diagnosties theory[2,3,7] because they are representative of this kind of model.
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[1] 王松桂,《线性模型的理论及其应用》,安徽教育出版社(1987). [2] Cook,R,D,and,S,Weisberg,Residuals and Influence in Regression,Chapman-Hall,New York(1982). [3] Andrews,D,F.and,D.Pregibon,Finding Outliers that Matter,.J.Rap,Stat,,Soc,B,40,(1978),85-93. [4] 杨虎,强影响的分布与稳定性度量,数学研究与评论,10(3)(1990),393-398. [5] Weisberg,S.,Applied Linear Regression,New York(1980). [6] Huber,P,,Robust Statistics,Wiley New York(1981). [7] 陈希孺、王松桂,《近代回归分析—原理方法及应用》,安徽教育出版社(1987). [8] 杨虎,Kantorovich不等式的延拓与均方误差比效率,应用数学.1(4)(1988),85-90. -
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