Bayes estimator for the inequality-constrained regression model*

Abstract

This article studies the Bayesian estimation of the inequality-constrained regression model under a balanced loss function. The usual Bayes estimator is often involved in some complex integrals and has no explicit expression, which causes the corresponding properties be difficult to describe. Based on the idea of linear Bayes method suggested by Rao (1973), the present paper constructs a linear Bayes estimator for the regression parameters without specify their specific prior distributions. It is proved that the proposed linear Bayes estimator outperforms the corresponding least squares estimator, and numerical simulations show that when there is collinearity in design matrix, the linear Bayes estimator performs better than the usual Bayes estimator.