一般线性模型下简单投影预测再研究  

Further Research on Simple Projection Predictor Under a General Linear Model

作　　者：姜波[1] 王路平[1] 田永革 JIANG Bo;WANG Luping;TIAN Yongge(College of Mathematics and Information Science,Shandong Technology and Business University,Yantai,Shandong,264005,P.R.China;College of Business and Economics,Shanghai Business School,Shanghai,201400,P.R.China)

机构地区：[1]山东工商学院数学与信息科学学院,山东烟台264005 [2]上海商学院商务经济学院,上海201400

出　　处：《数学进展》2024年第1期64-80,共17页Advances in Mathematics（China）

基　　金：山东省自然科学基金面上项目(No.ZR2019MA065)。

摘　　要：线性模型是统计学中一类重要的模型,模型中未知参数的估计和预测问题是统计推断工作中的基本问题.依据不同的评价标准,会得到不同形式的预测量,简单投影预测(SPP)形式简洁,最优线性无偏预测(BLUP)性质优良,自然会考虑这两个预测量之间的关系.本文给出最优线性无偏预测与简单投影预测相等的充要条件,最后研究了简单投影预测和最优线性无偏预测关于协方差矩阵的稳健性,利用统计学中的误差均匀相关模型来说明等价条件的具体应用.Linear model is a kind of important model in statistics.The estimation and prediction of unknown parameters in the model is a basic problem in statistical inference.According to different evaluation criteria,different forms of predictors are obtained.The simple projection prediction(SPP)has simple form,and the best linear unbiased prediction(BLUP)has very excellent properties.Naturally,the relationship between the two predictors are considered.We give the necessary and sufficient conditions for the equivalence of SPP and BLUP.Finally,we research the robustness of SPP and BLUP with respect to covariance matrix and illustrate the application of equivalence conditions by use of error uniform correlation models.

关 键 词：线性模型 简单投影预测 最优线性无偏预测 等价性 稳健性 

分 类 号：O212.1[理学—概率论与数理统计]