  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 the 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 (Sonderegger and Hannig 2014), 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.
