An overview of the estimation of large covariance and precision matrices

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.