多元正态分布方差阵的估计问题

Estimation Problems About Covariance Matrix of Multivariate Normal Distribution

设z_1,…,z_n是来自m维正态总体N_m(0,∑)的子样,本文在一个同变估计类D＝{h_1(w)A+h_2(w)yy':h_1,h_2为任意可测函数}(其中A=sumfrom n=1 to ∞(1\n)z_1z_2,y=n^(1/2)(?),(?)=1/n(z_1+...+z_n),W=y A^(-1)y)中讨论了方差阵z在损失函数L_1(∑δ)=tr(∑^(-1)δ)-l_n|∑^(-1)δ|-m和L_2(∑,δ)=tr(∑^(-1)δ-I)~2下的最优估计问题.

Let Xl, 晻? Xn are iid Normal (Nm(0, ))random vectors,, it is known that in the estimation classes D = {A; a is a con- and A are best estimatiors of under loss bunctions respectively. In this paper, we get the resuits that in the estimation classes D* = {h1(y'A-1y) ?A + h2y1A-1y) ·yy':h1,h2, are measurable funtions} A and A are best estimators of un- der loss functions L1 and L2 respectively.