林春土.一般Gauss—Markov模型下最小二乘估计是最佳估计的充要条件[J].数学研究及应用,1993,13(3):433~436
一般Gauss—Markov模型下最小二乘估计是最佳估计的充要条件
Necessary and Sufficient Conditions for the Least Squares Estimator to Be the Best Linear Unbiased Estimator in the General Gauss- Markov Model
投稿时间:1991-04-15  修订日期:1993-04-14
DOI:10.3770/j.issn:1000-341X.1993.03.021
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林春土 浙江大学 
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      In this paper, we discuss the decomposition of the space μ(X : V) and the invariance with respect to the choice of a generalized inverse of matrix X in the general Gauss-Markov model. In Theorem 1, we give necessary and sufficient conditions for the least squares estimator Pxy = BLUE(Xβ) under the general Gauss-Markov model M = {y,Xβ,σ2V}. In Theorem 2, we prove that Pxy= BLUE(Xβ) under model M and invariant with respect to the choice of a generalized inverse of matrix X are equivalent.
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