THREE RANK FORMULAS ASSOCIATED WITH THE COVARIANCE MATRICES OF THE BLUE AND THE OLSE IN THE GENERAL LINEAR MODEL

Simo Puntanen, George P.H. Styan and Yongge Tian ()

Econometric Theory, 2005, vol. 21, issue 3, 659-663

Abstract: In this paper we consider the estimation of the expectation vector Xβ under the general linear model {y,Xβ,σ2V}. We introduce a new handy representation for the rank of the difference of the covariance matrices of the ordinary least squares estimator OLSE(Xβ) (= Hy, say) and the best linear unbiased estimator BLUE(Xβ) (= 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 Hy and Gy can be characterized by the rank-subtractivity ordering between the covariance matrices of y and Hy. This rank characterization suggests a particular presentation for the rank of the difference of the covariance matrices of Hy and Gy. We show, however, that this presentation is valid if and only if the model is connected.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:21:y:2005:i:03:p:659-663_05

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