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An Overview on the Estimation of Large Covariance and Precision Matrices
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An Overview on the Estimation of Large Covariance and Precision Matrices

Jianqing Fan, Yuan Liao and Han Liu
ArXiv.org
Cornell University
04/12/2015
DOI: 10.48550/arxiv.1504.02995
url
https://doi.org/10.1111/ectj.12061View
Published (Version of record)This article has now been published in a journal and has been peer-reviewed by subject experts. This version may differ significantly from the preprint version. Access restricted to faculty, staff and students
url
https://doi.org/10.48550/arxiv.1504.02995View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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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.
Statistics - Methodology

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