关键词: 线性约束, 似然函数, 贝叶斯估计, 经验贝叶斯估计

Abstract: This paper firstly constructs the sample likelihood function of the multivariate linear regression model with linear restraint. We prove that this construction is reliable by Lagrange multiplier method. Secondly, we discuss the influence of linear constraints to model parameters from the perspective of likelihood function, and then make the Bayesian improvement and the empirical Bayesian improvement respectively to the estimation of model parameter by the traditional theory. Making the Bayesian improvement, we regard matrix normal-Wishart distribution as the joint conjugate prior distribution of model parameters. Combining this prior distribution with the constructed likelihood function to calculate the posterior distributions of these parameters, we get their Bayesian estimations. When doing the empirical Bayesian improvement, we classify the whole samples and discuss the influence of parametric estimations of these groups of samples to the model parametric estimation of the whole samples from the perspective of variance. We get empirical Bayesian estimations of these parameters. Finally, computer simulation is taken by Matlab software. The results show that both of the two improved estimations are more accurate than the model parametric estimation with the traditional theory. In the case of big data environment, this method computes faster than traditional one.

Key words: Linear Restraint, Likelihood Function, Bayesian Estimation, Empirical Bayesian Estimation