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一般线性模型中 BLUE 与普通最小二乘协方差矩阵的三个秩公式AI 解读

In this paper we consider the estimation of the expectation vector X β under the general linear model { y , X β,σ 2 V }. We introduce a new handy representation for the rank of the difference of the covariance matrices of the ordinary least squares estimator OLSE( X β) (= Hy , say) and the best linear unbiased estimator BLUE( X β) (= Gy , say). From this formula some well-known conditions for the equality between Hy and Gy follow at once. We recall that the equality between…

02.4.2 结构方程模型拟合优度检验中一个矩阵的秩：解答AI 解读

On the rank of a matrix useful in goodness-of-fit testing of structural equation models—solution.An excellent solution was independently proposed by A. Satorra and H. Neudecker, the posers of the problem.

02.1.2 特定对称幂等矩阵问题：解答AI 解读

It is easy to see that Problem 02.1.2 holds more generally in that the result is valid for B Hermitian complex (rather than “symmetric real”), for m = 0,1,…, q (rather than just for “ m < q ”), for r ≠ 0 (rather than just for “integer r > 1”), and for tr( B k ) = tr( C k ), k = 1,2,3,4 (rather than for “ k = 1,2,…”), as shown by Shanbhag (1970).

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