矩阵损失下多元统计中回归系数的线性Minimax估计

THE LINEAR MINIMAX ESTIMATOR OF REGRESSION COEFFICIENT IN MULTIVARITE STATISTICS UNDER MATRIX LOSS

设Ｙ１，Ｙ２…，Ｙｍ，ｉ．ｉ．ｄ，ＥＹ１＝Ｘβ，ｃｏｖＹ１＝∑，这里Ｘ已知，β和∑未知。在矩阵损失下，我们给出了ＳＸβ的线性估计在齐次（非齐次）线性估计类中的唯一的线性Ｍｉｎｉｍａｘ估计。

Let Y1,Y2… ,Ym, be i.i.d.,EY1 = Xβ,cov Y1 = ∑, wllereXis known, β ∈ Rp and ∑ > 0are unknown. We give a unique linear Mihanax estimator of linear estimator of SXβ in the class ofhomogeneous (non homogenous) linear chimator under matrix loss function.