Linear Bayesian estimators for linear models with constraints

Abstract

The paper employs a linear Bayesian procedure to simultaneously estimate regression parameters and variance parameter in a linear model with equality constraints. We obtain the expression of the linear Bayesian estimator (LBE) for the parameter vector, which consists of the regression parameters and the variance parameter, without specifying the specific form of the prior. The superiorities of the proposed LBE over some classical estimators are established in terms of mean squared error matrix criterion. Monte Carlo simulations and a numerical example are presented to compare its performances with those of the usual Bayesian estimator and the Lindley approximation as well.

Keywords:

• Equality constraints
• linear Bayesian estimator
• Gibbs sampling
• Lindley approximation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [11371051].