The Annals of Statistics

High-dimensional covariance matrix estimation in approximate factor models

Jianqing Fan, Yuan Liao, and Martina Mincheva

Full-text: Open access

Abstract

The variance–covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu [J. Amer. Statist. Assoc. 106 (2011) 672–684], taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Article information

Source
Ann. Statist., Volume 39, Number 6 (2011), 3320-3356.

Dates
First available in Project Euclid: 5 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1330958681

Digital Object Identifier
doi:10.1214/11-AOS944

Mathematical Reviews number (MathSciNet)
MR3012410

Zentralblatt MATH identifier
1246.62151

Subjects
Primary: 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 62F12: Asymptotic properties of estimators 62H12: Estimation

Keywords
Sparse estimation thresholding cross-sectional correlation common factors idiosyncratic seemingly unrelated regression

Citation

Fan, Jianqing; Liao, Yuan; Mincheva, Martina. High-dimensional covariance matrix estimation in approximate factor models. Ann. Statist. 39 (2011), no. 6, 3320--3356. doi:10.1214/11-AOS944. https://projecteuclid.org/euclid.aos/1330958681


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