A compound decision approach to covariance matrix estimation

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 high‐dimensional settings are common in modern genomics, where covariance matrix estimat...

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Bibliographic Details
Published in:Biometrics Vol. 79; no. 2; pp. 1201 - 1212
Main Authors: Xin, Huiqin, Zhao, Sihai Dave
Format: Journal Article
Language:English
Published: United States Blackwell Publishing Ltd 01.06.2023
Subjects:
Analysis of covariance
Animals
Bayes Theorem
Biostatistics
compound decision theory
Computer Simulation
Covariance matrix
Data analysis
Eigenvalues
Estimation
Gene Regulatory Networks
genes
Genomics
g‐modeling
Mice
nonparametric maximum likelihood
Nonparametric statistics
Research methodology
Sample Size
separable decision rule
sequence analysis
shrinkage
variance covariance matrix
g-modeling
separable decision rule
nonparametric maximum likelihood
compound decision theory
ISSN:0006-341X, 1541-0420, 1541-0420
Online Access:Get full text
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Summary: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 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.
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ISSN:0006-341X
1541-0420
1541-0420
DOI:10.1111/biom.13686