Ridge-type linear shrinkage estimation of the mean matrix of a high-dimensional normal distribution
Ridge-type linear shrinkage estimation of the mean matrix of a high-dimensional normal distribution
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DOI：
10.1016/j.jmva.2020.104608
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Ryota Yuasa;T. Kubokawa
中科院分区：
文献类型：
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作者：
Ryota Yuasa;T. Kubokawa
研究了在高维环境下多元正态分布均值矩阵的估计问题。考虑了精度矩阵的脊修正efron - morris型线性收缩估计，而不是Moore-Penrose广义逆，并根据二次损失下最小化Stein无偏风险估计来估计脊型线性收缩估计中的权值。利用随机矩阵理论证明了在高维贝叶斯模型中，具有估计权值的脊型线性收缩估计量是极小极大的，并且估计权值和具有这些估计权值的损失函数渐近等于最优对应项。对脊型线性收缩估计器的性能与现有的Efron-Morris和James-Stein估计器进行了数值比较。
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.