Shrinkage estimation of eigenvalues of covariance matrices for Gaussian spiked covariance models are known to be effective especially in high-dimensional problems. Various shrinkage methods have been proposed, and these typically employ nonlinear functions of eigenvalues of sample covariance matrices. Here we investigate Bayesian shrinkage methods for single-spiked covariance models. The choice of priors and the construction of the Bayes estimator are considered, and it is proved that the Bayes estimator of the present shrinkage prior dominates asymptotically that of the Jeffreys prior regarding the Kullback–Leibler risk. The Bayes estimators are obtained as the posterior mean of the covariance matrices. In numerical simulations, the Bayes methods based on the present shrinkage prior and the Jeffreys prior are compared with other non-Bayes methods.

已知高斯尖峰协方差模型的协方差矩阵特征值的收缩估计是有效的，尤其是在高维问题中。已经提出了各种收缩方法，并且这些方法通常采用样本协方差矩阵的特征值的非线性函数。在这里，我们研究单峰协方差模型的贝叶斯收缩方法。考虑了先验的选择和贝叶斯估计器的构造，事实证明，就Kullback-Leibler风险而言，当前收缩先验的贝叶斯估计器渐近地占杰弗里斯先验估计的贝叶斯估计器的主导。获得贝叶斯估计量作为协方差矩阵的后均值。在数值模拟中，将基于当前收缩先验和杰弗里斯先验的贝叶斯方法与其他非贝叶斯方法进行了比较。