An overview of the estimation of large covariance and precision matrices

Jianqing Fan; Yuan Liao; Han Liu

doi:10.1111/ectj.12061

journal article Feb 01, 2016

An overview of the estimation of large covariance and precision matrices

Jianqing Fan Yuan Liao

Han Liu

The Econometrics Journal Vol. 19 No. 1 pp. C1-C32 · Oxford University Press (OUP)

View at Publisher Save 10.1111/ectj.12061

Topics

No keywords indexed for this article. Browse by subject →

References

104

[1]

Ahn "Eigenvalue ratio test for the number of factors" Econometrica (2013) 10.3982/ecta8968

[2]

Ahn "The high‐dimension, low‐sample‐size geometric representation holds under mild conditions" Biometrika (2007) 10.1093/biomet/asm050

[3]

Aıt‐Sahalia (2015) 10.3386/w21584

[4]

Alessi "Improved penalization for determining the number of factors in approximate factor models" Statistics and Probability Letters (2010) 10.1016/j.spl.2010.08.005

[5]

Ang (2008) 10.2139/ssrn.1106463

[6]

Antoniadis "Wavelets in statistics: a review" Journal of the Italian Statistical Society (1997) 10.1007/bf03178905

[7]

Antoniadis "Regularization of wavelet approximations" Journal of the American Statistical Association (2001) 10.1198/016214501753208942

[8]

Bai "Inferential theory for factor models of large dimensions" Econometrica (2003) 10.1111/1468-0262.00392

[9]

Bai "Statistical analysis of factor models of high dimension" Annals of Statistics (2012) 10.1214/11-aos966

[10]

Bai "Determining the number of factors in approximate factor models" Econometrica (2002) 10.1111/1468-0262.00273

[11]

Banerjee "Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data" Journal of Machine Learning Research (2008)

[12]

Bickel "Covariance regularization by thresholding" Annals of Statistics (2008) 10.1214/08-aos600

[13]

Bickel "Simultaneous analysis of Lasso and Dantzig selector" Annals of Statistics (2009) 10.1214/08-aos620

[14]

Boivin "Understanding and comparing factor‐based forecasts" International Journal of Central Banking (2005)

[15]

Boivin "Are more data always better for factor analysis" Journal of Econometrics (2006) 10.1016/j.jeconom.2005.01.027

[16]

Breitung "GLS estimation of dynamic factor models" Journal of the American Statistical Association (2011) 10.1198/jasa.2011.tm09693

[17]

Cai "Adaptive thresholding for sparse covariance matrix estimation" Journal of the American Statistical Association (2011) 10.1198/jasa.2011.tm10560

[18]

Cai "Optimal rates of convergence for sparse covariance matrix estimation" Annals of Statistics (2012) 10.1214/12-aos998

[19]

Cai "A constrained ℓ1 minimization approach to sparse precision matrix estimation" Journal of the American Statistical Association (2011) 10.1198/jasa.2011.tm10155

[20]

Cai "Sparse PCA: optimal rates and adaptive estimation" Annals of Statistics (2013) 10.1214/13-aos1178

[21]

Campbell (1996)

[22]

Candès "The Dantzig selector: statistical estimation when p is much larger than n" Annals of Statistics (2007) 10.1214/009053606000001523

[23]

Candès "Exact matrix completion via convex optimization" Foundations of Computational Mathematics (2009) 10.1007/s10208-009-9045-5

[24]

Catoni "Challenging the empirical mean and empirical variance: a deviation study" Annales de l'Institut Henri Poincaré, Probabilités et Statistiques (2012) 10.1214/11-aihp454

[25]

Chamberlain "Arbitrage, factor structure, and mean‐variance analysis on large asset markets" Econometrica (1983) 10.2307/1912275

[26]

Choi "Efficient estimation of factor models" Econometric Theory (2012) 10.1017/s0266466611000338

[27]

Connor "Semiparametric estimation of a characteristic‐based factor model of stock returns" Journal of Empirical Finance (2007) 10.1016/j.jempfin.2006.10.001

[28]

Connor "Efficient semiparametric estimation of the Fama–French model and extensions" Econometrica (2012) 10.3982/ecta7432

[29]

Davis "The rotation of eigenvectors by a perturbation" Journal of Mathematical Analysis and Applications (1963) 10.1016/0022-247x(63)90001-5

[30]

Donoho "Wavelet shrinkage: asymptopia? (with discussion)" Journal of the Royal Statistical Society (1995) 10.1111/j.2517-6161.1995.tb02032.x

[31]

Doz "A quasi‐maximum likelihood approach for large, approximate dynamic factor models" Review of Economics and Statistics (2012) 10.1162/rest_a_00225

[32]

El Karoui "High‐dimensionality effects in the markowitz problem and other quadratic programs with linear constraints: risk underestimation" Annals of Statistics (2010) 10.1214/10-aos795

[33]

Fama "The cross‐section of expected stock returns" Journal of Finance (1992) 10.1111/j.1540-6261.1992.tb04398.x

[34]

Fan "Variable selection via nonconcave penalized likelihood and its oracle properties" Journal of the American Statistical Association (2001) 10.1198/016214501753382273

[35]

Fan "Statistical analysis of big data on pharmacogenomics" Advanced Drug Delivery Reviews (2013) 10.1016/j.addr.2013.04.008

[36]

Fan "Nonconcave penalized likelihood with a diverging number of parameters" Annals of Statistics (2004) 10.1214/009053604000000256

[37]

Fan "High dimensional covariance matrix estimation using a factor model" Journal of Econometrics (2008) 10.1016/j.jeconom.2008.09.017

[38]

Fan "Network exploration via the adaptive LASSO and SCAD penalties" Annals of Applied Statistics (2009) 10.1214/08-aoas215

[39]

Fan "High dimensional covariance matrix estimation in approximate factor models" Annals of Statistics (2011) 10.1214/11-aos944

[40]

Fan "Vast portfolio selection with gross‐exposure constraints" Journal of the American Statistical Association (2012) 10.1080/01621459.2012.682825

[41]

Fan "Large covariance estimation by thresholding principal orthogonal complements (with discussion)" Journal of the Royal Statistical Society (2013) 10.1111/rssb.12016

[42]

Fan "Challenges of big data analysis" National Science Review (2014) 10.1093/nsr/nwt032

[43]

Fan (2015)

[44]

Fan "Estimation of high‐dimensional mean regression in absence of symmetry and light‐tail assumptions" Journal of Royal Statistical Society (2016)

[45]

Fan "Projected principal component analysis in factor models" Annals of Statistics (2016) 10.1214/15-aos1364

[46]

Fang (1990) 10.1007/978-1-4899-2937-2

[47]

Forni "The generalized dynamic factor model: representation theory" Econometric Theory (2001) 10.1017/s0266466601176048

[48]

Forni "The generalized dynamic‐factor model: identification and estimation" Review of Economics and Statistics (2000) 10.1162/003465300559037

[49]

Frahm (2008)

[50]

Sparse inverse covariance estimation with the graphical lasso

Jerome Friedman, Trevor Hastie, Robert Tibshirani

Biostatistics 2008 10.1093/biostatistics/kxm045

Showing 50 of 104 references

Cited By

278

Eigenvector overlaps in large sample covariance matrices and nonlinear shrinkage estimators

Zeqin Lin, Guangming Pan · 2026

The Annals of Statistics

Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization

Xuran Meng, Yuan Cao · 2025

Journal of the American Statistical...

An Improved DCC Model Based on Large-Dimensional Covariance Matrices Estimation and Its Applications

Yu-Zhong Zhang, Jiyuan Tao · 2023

Symmetry

Certifiably optimal sparse inverse covariance estimation

Dimitris Bertsimas, Jourdain Lamperski · 2019

Mathematical Programming

Metrics

278

Citations

104

References

Details

Published: Feb 01, 2016
Vol/Issue: 19(1)
Pages: C1-C32
License: View

Authors

J

Jianqing Fan

Department of Operations Research and Financial Engineering, Princeton University Princeton College Park MD, 20742, USA

Y

Yuan Liao

Department of Mathematics, University of Maryland, College Park, MD 20742, USA

H

Han Liu

Department of Operations Research and Financial Engineering, Princeton University Princeton College Park MD, 20742, USA

Cite This Article

Jianqing Fan, Yuan Liao, Han Liu (2016). An overview of the estimation of large covariance and precision matrices. The Econometrics Journal, 19(1), C1-C32. https://doi.org/10.1111/ectj.12061

An overview of the estimation of large covariance and precision matrices

You May Also Like