线性回归模型中的KL型主成分估计  

KL-type principal component estimator in the linear regression model

作　　者：黄丹 黄介武 Huang Dan;Huang Jiewu(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《湖南文理学院学报（自然科学版）》2023年第2期7-14,共8页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：贵州省科技计划基金项目(黔科合基础[2017]1083);贵州省基础研究计划(软科学)(黔科合支[2019]20001)。

摘　　要：当线性回归模型中存在复共线性时,基于最小二乘估计的统计推断往往会受到影响。鉴于此,结合主成分估计和KL估计,提出了一类新的估计方法,即KL型主成分估计,以期克服复共线性问题。同时,得到新的估计在均方误差意义下优于最小二乘估计、主成分估计、r-k估计、r-d估计和KL估计的充要条件。并利用Monte Carlo模拟和实证分析对各估计量在均方误差准则下进行了比较。When there is multicollinearity in the linear regression model,statistical inference based on ordinary least square(OLS)estimator is often affected.To this end,a new estimator,KL-type principal component(KLPC)estimator,is proposed by combining principal component regression(PCR)estimator and KL estimator.Meanwhile,necessary and sufficient conditions for the superiority of the KLPC estimator over the OLS,PCR,r-k,r-d,and KL estimators in the mean squared error(MSE)criterion are derived.Furthermore,Monte Carlo simulation and empirical analysis are used to compare these estimators under the MSE criterion.

关 键 词：线性回归模型 复共线性 主成分估计 KL估计 均方误差 

分 类 号：O212.1[理学—概率论与数理统计]