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矩阵二次损失下的估计与矩阵超调和性AI 解读

Summary We investigate estimation of a normal mean matrix under the matrix quadratic loss. Improved estimation under the matrix quadratic loss implies improved estimation of any linear combination of the columns under the quadratic loss. First, an unbiased estimate of risk is derived and the Efron–Morris estimator is shown to be minimax. Next, a notion of matrix superharmonicity for matrix-variate functions is introduced and shown to have properties analogous to those of the…

尺度未知时多元正态均值向量的可容许估计量AI 解读

Summary We study admissibility of a subclass of generalized Bayes estimators of a multivariate normal vector in the case where the variance is unknown, under scaled quadratic loss. Minimaxity is established for some of these estimators.