正则矩阵回归的渐近性质  

ASYMPTOTICS FOR REGULARIZED MATRIX REGRESSIONS

作　　者：陈伟 CHEN Wei(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2022年第2期146-152,共7页Journal of Mathematics

摘　　要：本文研究了正则化矩阵回归估计量的渐进性质等问题.利用Knight,Fu和Chatterjee,Lahiri分别关于向量回归的Lasso估计量渐近性研究方法,推广到矩阵回归,研究核范数正则化矩阵回归估计量对应的渐近性质.从而得到了核范数矩阵估计量在随机误差二阶矩存在即E|∈_(I)|^(2)<∞的条件下的弱相合性和极限分布,以及在随机误差的低阶矩存在即E|∈_(I)|^(α)<∞,1<α<2的条件下,核范数矩阵参数估计量的强相合性以及对应的收敛速度.In this paper,we study the asymptotics properties of regularized matrix regressions estimators.We use Knight,Fu and Chatterjee,Lahiri’s asymptotics method on vector regressions,and extend it to matrix regressions to study the asymptotics properties of nuclear norm regularized matrix regressions estimators.We have obtained the weak consistency and limiting distribution of nuclear norm estimators when the second order moments of random errors exist,i.e.E|∈_(I)|^(2)<∞.And under the condition of the lower order moments of random errors existing,i.e.E|∈_(I)|^(α)<∞,1<α<2,we also have obtained the strong consistency and convergence rates of nuclear norm estimators.

关 键 词：渐近理论 线性回归 核范数 

分 类 号：O211.4[理学—概率论与数理统计]