矩阵损失下一般Gauss-Markov模型中回归系数的线性MINIMAX估计  

THE LINEAR MINIMAX ESTIMATE OF REGRESSION COEFFICIENT IN A GENEAL GAVSS-MARXOV MODEL UNDER MATRIX LOSS FUNCTION

作　　者：喻胜华[1] 

机构地区：[1]湖南大学应用数学系,长沙410082

出　　处：《系统科学与数学》1998年第2期234-238,共5页Journal of Systems Science and Mathematical Sciences

摘　　要：设Y是具有均值Xβ和协方差阵σ2V的n维随机向量，Sβ是线性可估函数，这里X，S和V0是已知矩阵，β∈Rp和σ2＞0是未知参数．本文在矩阵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, andSβ be a linear estimable fUnction, where X, S and V 0 are known matrices, β∈RP andσ2 > 0 are unknown parameters. In this paper tinder the matrix loss functions, the minimaxproperty of linear estimates is studied.Under suitable hypotheses, we obtain the unique linear minimax estimate of Sβ (We mustcomprehend uniqueness in the sense' almost everywhere' ).

关 键 词：矩阵损失 回归系数 高斯-马氏模型 线性估计 

分 类 号：O212.1[理学—概率论与数理统计]