矩阵正态分布均值矩阵的k-容许线性估计

The admissible linear estimates of the mean matrix on the similar normal distribution

本文考虑以下问题 :设 n× m随机矩阵 Y有分布 N(λn× m,Im φn× n) ,即 Vec( Y)服从均值向量为Vec( λ)、协方差矩阵为 I φ的多元正态分布 ,其中 λ为未知矩阵 ,I为单位阵 .本文讨论当 φ已知时 ,均值矩阵 λ的 k-容许线性估计 .

If n×m random matrix Y is distributed according to N(Θ_(n×m),V_(m×m)Σ_(n×n)),that is,Vec(Y) has a multivariate normal distribution with the mean vector Vec(Θ) and the corariarce matrix V_(m×m)Σ_(n×n), where Θ_(n×m) is unknown.We consider the k-admissible linear estimation of the mean matrix Θ_(n×m),when V_(m×m)Σ_(n×n) is known,this paper gives a necessary and sufficient condition for AY is the admissible linear estimates of the mean matrix of Θ on the similar normal distribution .