Abstract: In this paper, a linear Bayesian estimator is derived for the regression parameters in a linear model with equality constraints. The superiority of the linear Bayesian estimator over the constrained least square estimator is proved in terms of the mean square error matrix criterion. Monte Carlo simulations and a numerical example are employed to investigate the superiorities of the proposed linear Bayesian estimator.

Key words: equality constraints, linear Bayesian estimator, constrained least square estimator, mean square error matrix criterion, Monte Carlo simulation