矩阵正态变量均值二次型阵的估计

ESTIMATION OF THE QUADRATIC FORM MATRIX OF MATRIX NORMAL VARIBLE MEAN

文考虑了非中心 wishart 变量和非中心多元 F 变量的非中心参数阵的判决估计及其应用.本文考虑了更一般的矩阵正态变量均值二次型阵在二次损失下的判决估计问题,找出了优于其无偏估计的一类线性和非线性估计,推广了文的主要结果.

In paper,Muirhead considers the estimator of the noncentral parameter matrix in deci- sion-theoretic approach,which occurs in the noncentral Wishart,noncentral multivariate F,and their applications.In this paper,more generally,we consider general form of estimation of the quadratic form matrix of matrix normal variable mean under quadratic loss in decision-theoretic approch, and find out linear and nonlinear estimators which dominate their unbiased estimators,generalize the main results of paper.