二次损失下一般Gauss-Markov模型中可估函数的线性Minimax估计  

THE LINEAR MINIMAX ESTIMATORS OF ESTIMABLE FUNCTION IN A GENERAL GAUSS-MARKOV MODEL UNDER QUADRATIC LOSS FUNCTION

作　　者：喻胜华[1] 

机构地区：[1]湖南大学数学与计量经济学院,长沙410082

出　　处：《应用数学学报》2003年第4期693-701,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10101006号)

摘　　要：设Y是具有均值Xβ和协方差阵σ~2V的n维随机向量,Sβ是线性可估函数,这里X,S和V≥0是已知矩阵,β∈R^p和σ~2>0是未知参数。本文在二次损失下研究了线性估计的Minimax性。在适当的假设下,得到了Sβ的唯一线性Minimax估计(有关唯一性在几乎处处意义下理解)Let Y be a random n-vector with mean Xβ and covariance matrix σ2V, and S be a linear estimable function, where X, Sβ and V ≥ 0 are known matrics, ∈ Rp and σ ≥ 0 are unknown parameters. In this paper under the quadratic loss function, the minimax property of linear estimators is studied. Under suitable hypotheses, we obtain the unique linear minimax estimator of Sβ (We must comprehend uniqueness in the sense 'almost everywhere

关 键 词：二次损失 线性MINIMAX估计 可估函数 一般GAUSS-MARKOV模型 

分 类 号：O211.6[理学—概率论与数理统计]