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Activity Number:
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384
- Next-Generation Sequencing and High-Dimensional Data
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Type:
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Contributed
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Date/Time:
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Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
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Sponsor:
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Biometrics Section
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Abstract #318774
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Title:
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A Nonparametric Empirical Bayes Approach to Covariance Matrix Estimation
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Author(s):
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Huiqin Xin* and Sihai Dave Zhao
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Companies:
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Department of Statistics, University of Illinois at Urbana-Champaign and Department of Statistics, University of Illinois at Urbana-Champaign
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Keywords:
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Compound decision theory;
g-modeling;
nonparametric maximum likelihood;
separable decision rule
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Abstract:
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We propose an empirical Bayes method to estimate high-dimensional covariance matrices. Our procedure centers on vectorizing the covariance matrix and treating matrix estimation as a vector estimation problem. Drawing from the compound decision theory literature, we introduce a new class of decision rules that generalizes several existing procedures. We then use a nonparametric empirical Bayes g-modeling approach to estimate the oracle optimal rule in that class. This allows us to let the data itself determine how best to shrink the estimator, rather than shrinking in a pre-determined direction such as toward a diagonal matrix. Simulation results and a gene expression network analysis shows that our approach can outperform a number of state-of-the-art proposals in a wide range of settings, sometimes substantially.
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Authors who are presenting talks have a * after their name.
