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

作　　者：喻胜华[1] 何灿芝[1] 

机构地区：[1]湖南大学数学与计量经济学院,长沙410082

出　　处：《应用概率统计》2003年第2期203-209,共7页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(10101006)

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。本文分别在给定的矩阵损失和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 Sβ be a linear estimable function, where X, S and V > 0 are known matrices, β∈ RP and σ2 > 0 are unknown parameters. In this paper under the given matrix loss function and quadratic loss function, the minimax property of linear estimators is studied respectively. Under suitable hypotheses, we obtain the unique linear minimax estimator of Sβ(We must comprehend uniqueness in the sense ' almost everywhere ').

关 键 词：矩阵损失 二次损失 可估函数 MINIMAX估计 

分 类 号：O212.4[理学—概率论与数理统计]