Stable estimation of a covariance matrix guided by nuclear norm penalties

Eric C. Chi and Kenneth Lange

Computational Statistics & Data Analysis, 2014, vol. 80, issue C, 117-128

Abstract: Estimation of a covariance matrix or its inverse plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. The current paper introduces a novel prior to ensure a well-conditioned maximum a posteriori (MAP) covariance estimate. The prior shrinks the sample covariance estimator towards a stable target and leads to a MAP estimator that is consistent and asymptotically efficient. Thus, the MAP estimator gracefully transitions towards the sample covariance matrix as the number of samples grows relative to the number of covariates. The utility of the MAP estimator is demonstrated in two standard applications–discriminant analysis and EM clustering–in challenging sampling regimes.

Keywords: Covariance estimation; Regularization; Condition number; Discriminant analysis; EM clustering (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:80:y:2014:i:c:p:117-128

DOI: 10.1016/j.csda.2014.06.018

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