异协差阵下多因变量线性回归模型的平均估计  

Model Averaging of Multivariate Linear Regression Models with Heteroscedastic Covariance Matrix

作　　者：曲天尧 宋明辉 QU Tianyao;SONG Minghui(School of Mathematical Sciences,Capital Normal University,Beijing 100048)

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《系统科学与数学》2024年第10期3115-3132,共18页Journal of Systems Science and Mathematical Sciences

摘　　要：统计模型平均方法是统计学研究领域一个备受关注的热点问题,它可以有效地提高统计预测的精度.在统计学中,多因变量线性回归模型是一类重要并且实用的线性统计模型,文章主要研究当随机误差矩阵各行间协差阵不全相等时这类模型的平均方法.文章通过寻找一个矩阵用以将各行的异协差阵“统一化”,进而在马氏距离的基础上通过删组交叉验证的方法得到了相应的Mahalanobis CV权重选择准则,并证明了相应模型平均估计的渐近最优性.仿真研究表明,新方法在一般情况下要优于S-AIC、S-BIC、含有单个因变量的线性回归模型的MMA和JMA以及多因变量线性回归模型的MMMA等模型平均方法.The average method of statistical model is a hot issue in the field of statistics research,which can effectively improve the accuracy of statistical prediction.In statistics,multivariate linear regression model is a kind of important and practical linear statistical model.This paper mainly studies the average method of this kind of model when the random error matrix is not completely equal.We find a matrix to“unify”the different covariance matrices of each line,and then obtain the corresponding Mahalanobis CV weight selection criteria based on Mahalanobis distance by cross-validation method,and prove the asymptotic optimality of the average estimation of the corresponding model.Simulation results show that the new method is better than S-AIC,S-BIC,MMA and JMA of linear regression model with single dependent variable and MMMA of multivariate linear regression model in general.

关 键 词：多因变量线性回归模型 异协差阵 MCV准则 渐近最优性 

分 类 号：O212.1[理学—概率论与数理统计]