Review Articles

Covariance estimation via fiducial inference

W. Jenny Shi ,

Financial Planning & Analysis, MassMutual, Boston, MA, USA

Jan Hannig ,

Department of Statistics & Operations Research, University of North Carolina, Chapel Hill, NC, USA

Randy C. S. Lai ,

Department of Statistics, University of California, Davis, CA, USA

Thomas C. M. Lee

Department of Statistics, University of California, Davis, CA, USA

Pages 316-331 | Received 23 May. 2020, Accepted 10 Jan. 2021, Published online: 15 Nov. 2021,
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As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and Bayesian frameworks. Aiming to quantify the uncertainty of the estimators without having to choose a prior, we have developed a fiducial approach to the estimation of covariance matrix. Built upon the Fiducial Berstein–von Mises Theorem, we show that the fiducial distribution of the covariate matrix is consistent under our framework. Consequently, the samples generated from this fiducial distribution are good estimators to the true covariance matrix, which enable us to define a meaningful confidence region for the covariance matrix. Lastly, we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.


To cite this article: W. Jenny Shi, Jan Hannig, Randy C. S. Lai & Thomas C. M. Lee (2021)
Covariance estimation via fiducial inference, Statistical Theory and Related Fields, 5:4, 316-331,
DOI: 10.1080/24754269.2021.1877950
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