Covariance estimation via fiducial inference  

作　　者：W.Jenny Shi Jan Hannig Randy C.S.Lai Thomas C.M.Lee 

机构地区：[1]Financial Planning&Analysis,MassMutual,Boston,MA,USA [2]Department of Statistics&Operations Research,University of North Carolina,Chapel Hill,NC,USA [3]Department of Statistics,University of California,Davis,CA,USA

出　　处：《Statistical Theory and Related Fields》2021年第4期316-331,共16页统计理论及其应用（英文）

基　　金：Shi’s research was supported in part by the National Library of Medicine Institutional Training Grant T15 LM009451;Hannig’s research was supported in part by the National Sci-ence Foundation(NSF)under Grant Nos.1512945,1633074,and 1916115;Lee’s research was supported in part by the NSF under Grant No.1512945 and 1513484.

摘　　要：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.

关 键 词：covariance estimation SPARSITY fiducial inference CLIQUES 

分 类 号：O57[理学—粒子物理与原子核物理]