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Stable estimation of a covariance matrix guided by nuclear norm penalties

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  • Chi, Eric C.
  • Lange, Kenneth

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.

Suggested Citation

  • Chi, Eric C. & Lange, Kenneth, 2014. "Stable estimation of a covariance matrix guided by nuclear norm penalties," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 117-128.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:117-128
    DOI: 10.1016/j.csda.2014.06.018
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    References listed on IDEAS

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    Cited by:

    1. Zheng, Bang Quan, 2021. "RGLS and RLS in Covariance Structure Analysis," SocArXiv aejgf, Center for Open Science.
    2. Carel F. W. Peeters & Mark A. Wiel & Wessel N. Wieringen, 2020. "The spectral condition number plot for regularization parameter evaluation," Computational Statistics, Springer, vol. 35(2), pages 629-646, June.

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