Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high-dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g-modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA-seq experiment in mouse show that our approach is comparable to or can outperform a number of state-of-the-art proposals.

翻译：共变矩阵估算在许多应用中是一项基本的统计任务,但样本共变矩阵是次最佳的,如果抽样规模与特征数量相似或少于特征数量。这种高维设置在现代基因组学中很常见,因为共变矩阵估算经常被用作推算基因网络的一种方法。为了在这些设置中实现估算准确性,现有方法通常假设人口共变矩阵具有某种特定结构,例如孔径,或者采用缩放来更好地估算人口均值。本文中,我们研究了一种估算高维共变矩阵的新方法。我们首先将共变矩阵估算作为复杂的决定问题来框架。这促使确定决策规则的类别,并使用非参数性的经验性海湾模型方法来估算该类的最佳规则。在鼠标的RNA等值实验中,模拟结果和基因网络的推断表明,我们的方法可以与一些最先进的建议相比,或者可以超越一些最先进的建议。