Abstract
Abstract In the linear model Y = Xβ + e, with arbitrary covariance matrix V, relationships between SLSEs, WLSEs and BLUEs are developed. An explicit new expression for BLUEs in terms of WLSEs and eigenvectors of V associated with positive eigenvalues is presented. Reduction of WLSEs to SLSEs and BLUEs to WLSEs is also considered. This varies from Zyskind's work primarily by stressing positive eigenvalues. The same concentration on positive eigenvalues leads to a refinement of conditions under which m′Y is a BLUE.
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