On Conditions for Equality of OLSE,GLSE and MLE in Analysis of Covariance Structures

Abstract

For all covariance matrices with linear struture, a necessary and sufficient condition for OLSE to be equivalent to GLSE and MLE is shown. For spectrally decomposable class of covariance matrices, Σ, the GLSE with V = Σ^-1, MLE and OLSE are shown to be equivalent. In case of intraclass Σ such equivalence is true for any intraclass V. The implications of the results are discussed.