聚集数据多元线性模型参数的多元广义聚集双参数广义岭估计的相对效率  

The Relative Efficiency of Generalized Ridge Estimation for Multivariate Generalized Aggregation Doubleparameters of Multivariate Linear Model with Aggregated Data

作　　者：余新宏 郑剑平 王礼霞 YU Xinhong;ZHENG Jianping;WANG Lixia(Basic Course Teaching Department,Hefei University of Economics,Hefei Anhui 230011,China)

机构地区：[1]合肥经济学院基础课教学部,安徽合肥230011

出　　处：《上饶师范学院学报》2024年第3期1-7,66,共8页Journal of Shangrao Normal University

基　　金：2022年度安徽省高校自然科学研究项目(2022AH052621);2024年度安徽省科研计划编制项目(2024AH051542)。

摘　　要：复共线性聚集数据模型的岭估计过于强调参数的稳定性,而忽略了参数的无偏性。针对这个问题,采用施坦(Stein)压缩、广义岭(Liu)型估计等处理方法,提出聚集数据线性模型参数的多元广义聚集双参数的广义岭估计[Bh(K,D)=(X′T′TX+hI)-1(X′T′TX+QDQ′)(X′T′TX+QKQ′)-1X′T′TY],讨论多元广义聚集双参数改进估计的优良性,证明其两种相对效率的问题,最后推导出这两种相对效率的上界。The ridge estimation of the multicollinearity aggregated data model overly emphasized the stability of parameters and ignored their unbiasedness.In response to this problem,based on Liu-type and Stein-type compression~estimation method,generalized ridge estimation [Bh(K,D)=(X′T′TX+hI)-1(X′T′TX+QDQ′)(X′T′TX+QKQ′)-1X′T′TY] of multivariate generalized aggregation doubleparameters for linear model parameters of aggregated data was proposed,the superiority of the improved estimation of multivariate generalized aggregated dual parameters was discussed,and the two relative efficiencies were proved.Finally,the upper bounds of these two relative efficiencies were derived.

关 键 词：聚集数据 多元广义聚集 广义岭估计 相对效率 

分 类 号：O212.4[理学—概率论与数理统计]