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.
