Invariance of the BLUE under the linear fixed and mixed effects models
Keywords: best linear unbiased estimator, Gauss-Markov model, equality of the BLUEs, linear fixed effects model, linear mixed effects model, partitioned linear model
We consider the estimation of the parametric function X1β1 under the partitioned linear fixed effects model y=X1β1+X2β2+ε and the linear mixed effects model y=X1β1+X2γ2+ε, where γ2 is considered to be a random vector. Particularly, we consider when the best linear unbiased estimator, BLUE, of X1β1 under the linear fixed effects model equals the corresponding BLUE under the linear mixed effects model.
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