An Overview on the Estimation of Large Covariance and Precision Matrices

2015/04/12 by Jianqing Fan, Yuan Liao, Fan, Jianqing +3 · 5 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.1504.02995

openalex publication_date 2015/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance 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 estimating large covariance and precision matrices. We focus on two general approaches: rank based method and factor model based method. Theories and applications of both approaches are presented. These methods are expected to be widely applicable to analysis of economic and financial data.

Citations

• Surprising Asymptotic Conical Structure in Critical Sample Eigen-Directions
• Nearly unbiased variable selection under minimax concave penalty
• Nonconcave penalized likelihood with a diverging number of parameters
• A well-conditioned estimator for large-dimensional covariance matrices
• Nuclear norm penalization and optimal rates for noisy low rank matrix\n completion

Cited by

• Spectra of high-dimensional Spearman correlation matrices under scale-mixture dependence
• High dimensional matrix estimation through elliptical factor models
• Diffusion differentiable resampling
• Estimation of Semiparametric Factor Models with Missing Data
• Bayesian Graphical Models under Positivity Constraints: A Scalable generalized likelihood Approach

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