Open AccessAn overview of the estimation of large covariance and precision matrices
Author(s) -
Fan Jianqing,
Liao Yuan,
Liu Han
Publication year - 2016
Publication title -
the econometrics journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.861
H-Index - 36
eISSN - 1368-423X
pISSN - 1368-4221
DOI - 10.1111/ectj.12061
Subject(s) - covariance , estimation , estimation of covariance matrices , covariance intersection , computer science , mathematics , econometrics , statistics , engineering , systems engineering
Summary The estimation of large covariance and precision matrices is fundamental in modern multivariate analysis. However, problems arise from the statistical analysis of large panel economic and financial data. The covariance matrix reveals marginal correlations between variables, while the precision matrix encodes conditional correlations between pairs of variables given the remaining variables. In this paper, we provide a selective review of several recent developments on the estimation of large covariance and precision matrices. We focus on two general approaches: a rank‐based method and a factor‐model‐based method. Theories and applications of both approaches are presented. These methods are expected to be widely applicable to the analysis of economic and financial data.