中文摘要：

本文首先构造线性约束条件下的多元线性回归模型的样本似然函数，利用Lagrange法证明其合理性。其次，从似然函数的角度讨论线性约束条件对模型参数的影响，对由传统理论得出的参数估计做出贝叶斯与经验贝叶斯的改进。做贝叶斯改进时，将矩阵正态-Wishart分布作为模型参数和精度阵的联合共轭先验分布，结合构造的似然函数得出参数的后验分布，计算出参数的贝叶斯估计；做经验贝叶斯改进时，将样本分组，从方差的角度讨论由子样本得出的参数估计对总样本参数估计的影响，计算出经验贝叶斯估计。最后，利用Matlab软件生成的随机矩阵做模拟。结果表明，两种改进后的参数估计均较由传统理论得出的参数估计更精确、拟合结果的误差比更小、可信度更高，在大数据的情况下，改进后的计算方法速度更快。

英文摘要：

Tthis 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.