线性模型参数向量的近似贝叶斯估计

用线性贝叶斯方法去同时估计线性模型中回归系数和误差方差,并在不知道先验分布具体形式的情况下,得到了线性贝叶斯估计的表达式.在均方误差矩阵准则下,证明了其优于最小二乘估计和极大似然估计.与利用MCMC算法得到的贝叶斯估计相比,线性贝叶斯估计具有显式表达式并且更方便使用.对于几种不同的先验分布,数值模拟结果表明线性贝叶斯估...

Approximate Bayesian estimator for parameter vector in normal linear model

In this paper, the linear Bayesian method is employed to estimate regression coefficient and error variance simultaneously in a linear model and the expression of linear Bayesian estimator(LBE) is obtained without specifying the specific form of the prior. It is proved that the LBE is superior to the ordinary least square estimator and the maximum likelihood estimator in terms of mean square error matrix criterion. The LBE not only has an explicit expression but is more convenient to use than the Bayesian estimator(BE) obtained by using MCMC algorithm. Numerical simulations show that the LBE is closer to the true value than the BE for several different priors. Further, compared with the Lindley approximation, the LBE has a better estimation effect. Hence, both theoretical analysis and numerical simulations show that the LBE is an effective and feasible estimator.