Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model

Abstract

A linear mixed model ($\LMM$) $\M :\yy = \mxX\BETA + \mxZ\uu + \EPS $ with general assumptions and its transformed model $\T:\mxT\yy = \mxT\mxX\BETA + \mxT\mxZ\uu + \mxT\EPS $ are considered. This work concerns the comparison problem of predictors under $\M$ and $\T$. Our aim is to establish equality relations between the best linear unbiased predictors ($\BLUP$s) of unknown vectors under two $\LMM$s $\M$ and $\T$ through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.