On a matrix identity associated with generalized least squares

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Abstract

This note discusses an identity which is useful in the construction of reduced generalized least-squares equations, in the REML method of estimating variance components, and in calculating best linear unbiased predictors. The identity is shown to be a singular form of a better-known matrix relation. Some applications of the result are presented.

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The authors would like to thank Professor D.R. Cox for drawing the reference Pukelsheim (1976) to their attention, and Professor G.P.H. Styan for his interest, for pointing out further references and for suggesting a better proof of the limiting result.

Partial support from NSF DMS-8802378 is gratefully acknowledged.