A Compound Decision Approach to Covariance Matrix Estimation
Abstract
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such highdimensional 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 highdimensional 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 gmodeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNAseq experiment in mouse show that our approach is comparable to or can outperform a number of stateoftheart proposals.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.04549
 Bibcode:
 2020arXiv200504549X
 Keywords:

 Statistics  Methodology;
 Mathematics  Statistics Theory;
 62C12 (Primary) 62C25 (Secondary)
 EPrint:
 20 pages, 4 figures. Biometrics (2022)