More on BLU estimation in regression models with possibly singular covariances (Q1083808)

Consider the general linear regression model \(E(y)=A\beta\), \(Cov(y)=V\), where y is an \(n\times 1\) vector of observations, A is a known real \(n\times m\) matrix, and V is a known dispersion matrix. No rank assumptions are imposed on A or V. The aim of this paper is to investigate the class of all those matrices G leading to traditional BLUEs CGy for all estimable linear functions \(C\beta\), and to discuss its relations with two other sets introduced respectively by \textit{A. Albert} [SIAM J. Appl. Math. 24, 182-287 (1973; Zbl 0232.62030)] and by \textit{S. K. Mitra} and \textit{B. J. Moore} [Sankhyā, Ser. A 35, 139-152 (1973; Zbl 0277.62044)].