Upper Bounds for the Euclidean Distances Between the BLUEs Under the Partitioned Linear Fixed Model and the Corresponding Mixed Model

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Indian Statistical Institute Series


We consider the partitioned fixed effects linear model F: y= X1β1+ X2β2+ ε and the corresponding mixed model M: y= X1β1+ X2u+ ε, where ε is a random error vector and u is a random effect vector, i.e., M is obtained from F by replacing the fixed effects β2 with the random effects u. In this paper, we establish upper bounds for the Euclidean norm of the difference between the BLUEs of an estimable parametric function of β1 under models F and M. Some corresponding bounds are considered also for the difference between the ordinary least squares estimators, OLSEs.

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