Abstract The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron–Morris-type linear shrinkage estimators with ridge modification for the precision matrix instead of the Moore–Penrose generalized inverse are considered, and the weights in the ridge-type linear shrinkage estimators are estimated in terms of minimizing the Stein unbiased risk estimators under the quadratic loss. It is shown that the ridge-type linear shrinkage estimators with the estimated weights are minimax, and that the estimated weights and the loss function with these estimated weights are asymptotically equal to the optimal counterparts in the Bayesian model with high dimension by using the random matrix theory. The performance of the ridge-type linear shrinkage estimators is numerically compared with the existing estimators including the Efron–Morris and James–Stein estimators.

中文翻译：

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高维正态分布均值矩阵的脊型线性收缩估计

摘要 在高维设置中解决了多元正态分布的均值矩阵的估计问题。Efron-Morris 型线性收缩估计量对精度矩阵进行了脊修正而不是 Moore-Penrose 广义逆，并根据最小化 Stein 无偏风险估计量来估计脊型线性收缩估计量中的权重。二次损失。结果表明，具有估计权重的脊型线性收缩估计器是极大极小，并且估计权重和具有这些估计权重的损失函数通过使用随机矩阵渐近地等于高维贝叶斯模型中的最优对应物理论。