【摘要】 在线性模型中,当先验分布中超参数部分未知时,构造了回归系数和误差方差的同时参数型经验Bayes估计(PEBE).在均方误差矩阵(MSEM)准则下,讨论了回归系数的PEBE相对于最小二乘估计(LSE)的优良性;在均方误差(MSE)准则下讨论了误差方差的PEBE相对于其LSE的优良性.当先验分布中超参数全部未知时,重新构造了回归系数和误差方差的同时PEBE,并给出了它们在MSE准则下相对LSE优良性的模拟结果.更多还原

【Abstract】 When the hyperparameters of prior distribution are partly known in linear model, the simultaneous parametric empirical Bayes estimators (PEBE) of the regression coefficients and error variance are constructed. The superiority of PEBE over the least squares estimator (LSE) of regression coefficients is investigated in terms of the the mean square error matrix (MSEM) criterion, and the superiority of PEBE over LSE of the error variance is discussed under the the mean square error (MSE) criterion. Finally, when all hyperparameters are unknown, the PEBE of regression coefficients and error variance are reconstructed and the superiority of them over LSE under the MSE criterion are studied by simulation methods.更多还原