多元响应线性回归模型的马氏Mallows模型平均方法改进

Improvement of Mahalanobis Mallows Model Averaging Method for Multivariate Response Linear Regression Models

针对多元响应线性回归模型,提出了修改的马氏Mallows模型平均(MMMAc)方法。为了更充分地利用多元响应变量之间的相关性信息从而更好地提高预测精度,组合权重选择准则的构造同样考虑了马氏距离预测风险,并通过构造Wishart分布,推导出预测损失的无偏估计作为权重的选择准则,最终得到的MMMAc准则相比马氏Mallows模型平均(MMMA)准则增加了一个偏差矫正项,减小了对预测损失估计的偏差,因此通过最小化该准则得到的权重估计能更接近不可得的理论最优组合权重;最后,模拟对比实验验证了MMMAc方法的优势:MMMAc估计具有与MMMA估计同样的渐进最优性,因此两者的表现在大样本情形下没有太大差异,然而,由于修改后的权重选择准则为预测损失的无偏估计,因此在样本量不足的情形下,MMMAc方法的预测表现更佳。

A corrected Mahalanobis Mallows model averaging(MMMAc)method was proposed for the multivariate response linear regression model.In order to make full use of the correlation information among multivariate response variables and improve the prediction accuracy,Mahalanobis distance prediction risk was also considered in the construction of combinational weight selection criteria.And by constructing the Wishart distribution,the unbiased estimate of predicted loss was derived as the selection criterion of weight.Compared with the original MMMA criterion,the resulting MMMAc added a bias correction term,which reduced the bias in the prediction loss estimation.Therefore,the weight estimation obtained by minimizing this criterion was closer to the theoretical optimal combination weight that is not available.Finally,the simulation and comparison experiments verified the advantages of the MMMAc method:the MMMAc estimation has the same asymptotic optimality as the MMMA estimation,so there is no significant difference in their performance in the large sample case;however,since the modified weight selection criterion is an unbiased estimate of the prediction loss,the MMMAc method performs better in the case of insufficient sample size.