摘要
对任意矩阵X,X(X′X)-X′与广义逆(X′X)-的选取无关,且有X=X(X′X)-X′X,X′=X′X(X′X)-X′.本文拓展了上述结果,证明了对任意正定阵V,X(X′V-1X)-X′V-1与广义逆(X′V-1X)-的选取无关,并有X=X(X′V-1X)-X′V-1X,X′=X′V-1X(X′V-1X)-X′.利用上述推广的结果,直接给出了广义线性模型中可估函数c′β的最小二乘估计c′β*的唯一性和无偏性的证明.
As well known, for a random matrix X, the choose of the generalized inverse （X＇X）^- is nothing to do with X （ X＇ X ）^- X＇ , and X = X（ X＇ X ）^- X＇ X , X＇ = X＇ X （ X＇ X ）^- X＇ . In this paper, we extend these results and prove that the generalized inverse （ X＇ V^-1X）^- is nothing to do with X （ X＇ V^- 1 X） - X＇ V^- 1 for a random definite matrix V, and we have X = X（ X＇ V ~ 1 X） - X＇ V- 1 X, X＇ = X＇ V- 1 X （ X＇ V- 1 X ）^- X＇. Using this generalization, we obtain a direct proof of the uniqueness and unbiasedness on the least square estimate c＇β＊ of the estimable function c＇β＊ in the generalized linear models.
出处
《南阳师范学院学报》
CAS
2006年第3期17-18,共2页
Journal of Nanyang Normal University
关键词
广义逆
广义线性模型
最小二乘估计
generalized inverse
generalized linear model
the least square estimate
