ESTIMATION　OF　SCATTER　MATRIX　BASED　ON　i．i．d．　SAMPLE　FROM　ELLIPTICAL　DISTRIBUTIONS  

作　　者：方开泰 李润泽 

出　　处：《Acta Mathematicae Applicatae Sinica》1995年第4期405-412,共8页应用数学学报（英文版）

摘　　要：In this paper, we consider the estimation of a scatter matrix under entropy loss, quadratic loss, when the samples x(1),…,x(n) are i.i.d. and x(1)￣ECp(μ,Σ,f). With respect to entropy and quadratic losses, we obtain the best estimator of Σ having the form αSx as well as having the form Tx△Tx' , where Sx,Tx and △ are given in the text, and obtain the minimax estimator of Σ and the best equivariant estimator of Σ with respect to the triangular transformations group LT+ (p)(the group consisting of lower triangular matrices with positive diagonal elements). Some related discussion are given as its generalizations.In this paper, we consider the estimation of a scatter matrix under entropy loss, quadratic loss, when the samples x(1),…,x(n) are i.i.d. and x(1)￣ECp(μ,Σ,f). With respect to entropy and quadratic losses, we obtain the best estimator of Σ having the form αSx as well as having the form Tx△Tx' , where Sx,Tx and △ are given in the text, and obtain the minimax estimator of Σ and the best equivariant estimator of Σ with respect to the triangular transformations group LT+ (p)(the group consisting of lower triangular matrices with positive diagonal elements). Some related discussion are given as its generalizations.

关 键 词：Elliptical distribution entropy loss quadratic loss 

分 类 号：O211[理学—概率论与数理统计]