协方差阵扰动对Stein岭型主成分估计的影响分析  

Influence analysis of covariance matrix disturbance on stein ridge type principal component estimator

作　　者：朱宁[1,2] 黄荣臻 张茂军 邓超海[1] Zhu Ning;Huang Rongzhen;Zhang Maojun;Deng Chaohai(School of Mathematics and Computing Science,Guilin University of Electronic Science and Technology,Guilin 541004,China;Institute of Information Technology of Guet,Guilin University of Electronic Science and Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]桂林电子科技大学信息科技学院,广西桂林541004

出　　处：《河南师范大学学报（自然科学版）》2019年第2期1-7,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(71461005);广西研究生教育创新计划资助项目(YCSW2017143)

摘　　要：针对线性回归模型中协方差阵扰动对Stein岭型主成分估计β(P)G的影响问题进行研究.证明了β(P)G的某种极限是数据删除模型的Stein岭型主成分估计;建立了β(P)G与G-M模型的Stein岭型主成分估计β(P)之间的关系;定义了度量扰动影响的距离测度DG,并给出了DG的多种计算式;最后通过实例验证其有效性.In this paper,the issue of influence analysis of covariance matrix disturbance on stein ridge type principal components estimator(SRPCE)in linear regression model is studied.We prove that in the data deletion model,some limit of SRPCE which in the regression model with covariance matrix disturbance is SRPCE.Then,we set up the relationships among(P)G and(P).Next,we define the distance measure D G,which can be assessed the disturbing influence.Afterwards,we give several calculation formulas of D G.Finally,a practical example is presented to illustrate the effectiveness of this method.

关 键 词：Stein岭型主成分估计 协方差阵扰动模型 数据删除模型 影响分析 COOK距离 

分 类 号：O212.1[理学—概率论与数理统计]