Covariance estimation via fiducial inference

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 fiducia...

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Published inStatistical theory and related fields Vol. 5; no. 4; pp. 316 - 331
Main Authors Jenny Shi, W., Hannig, Jan, Lai, Randy C. S., Lee, Thomas C. M.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.10.2021
Taylor & Francis Group
Subjects
cliques
covariance estimation
fiducial inference
Primary 62J10
Secondary 62F12
sparsity
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Summary: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.
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ISSN:2475-4269
2475-4277
2475-4277
DOI:10.1080/24754269.2021.1877950