Abstract: It was proved that the Bayesian linear unbiased estimator
of the unknown parameters in a general linear model under the
quadratic loss function is also the Bayesian linear unbiased
estimator under the matrix loss function. The robustness of the
Bayesian linear unbiased estimator of the unknown parameter in terms
of error distributions was also discussed; moreover, the necessary
and sufficient conditions are obtained, under which the Bayesian
linear unbiased estimator of the unknown parameters hold its
optimality.

Key words: linear model, Bayesian linear unbiased estimator, robustness