As a classical problem,covariance estimation has drawn much attention from the statistical com-munity for decades.Much work has been done under the frequentist and Bayesian frameworks.Aiming to quantify the uncertaint...As a classical problem,covariance estimation has drawn much attention from the statistical com-munity 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 distri-bution 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.展开更多
基金Shi’s research was supported in part by the National Library of Medicine Institutional Training Grant T15 LM009451Hannig’s research was supported in part by the National Sci-ence Foundation(NSF)under Grant Nos.1512945,1633074,and 1916115Lee’s research was supported in part by the NSF under Grant No.1512945 and 1513484.
文摘As a classical problem,covariance estimation has drawn much attention from the statistical com-munity 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 distri-bution 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.
