Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for both statistical problems: nonlinear shrinkage of the eigenvalues of the sample covariance matrix. The optimal nonlinear shrinkage formula depends on unknown population quantities and is thus not available. It is, however, possible to consistently estimate an oracle nonlinear shrinkage, which is motivated on asymptotic grounds. A key tool to this end is consistent estimation of the set of eigenvalues of the population covariance matrix (also known as the spectrum), an interesting and challenging problem in its own right. Extensive Monte Carlo simulations demonstrate that our methods have desirable finite-sample properties and outperform previous proposals.
|Date of creation:||Jan 2013|
|Date of revision:||Jul 2013|
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- Ledoit, Olivier & Wolf, Michael, 2004.
"A well-conditioned estimator for large-dimensional covariance matrices,"
Journal of Multivariate Analysis,
Elsevier, vol. 88(2), pages 365-411, February.
- Ledoit, Olivier & Wolf, Michael, 2000. "A well conditioned estimator for large dimensional covariance matrices," DES - Working Papers. Statistics and Econometrics. WS 10087, Universidad Carlos III de Madrid. Departamento de Estadística.
- Connor, Gregory & Korajczyk, Robert A, 1993. " A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
- Anatolyev, Stanislav, 2012.
"Inference in regression models with many regressors,"
Journal of Econometrics,
Elsevier, vol. 170(2), pages 368-382.
- Stanislav Anatolyev, 2009. "Inference in Regression Models with Many Regressors," Working Papers w0125, Center for Economic and Financial Research (CEFIR).
- Roll, Richard & Ross, Stephen A, 1980. " An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
- Theodoros Tsagaris & Ajay Jasra & Niall Adams, 2010. "Robust and Adaptive Algorithms for Online Portfolio Selection," Papers 1005.2979, arXiv.org.
- Khan, Mozaffar, 2008. "Are accruals mispriced Evidence from tests of an Intertemporal Capital Asset Pricing Model," Journal of Accounting and Economics, Elsevier, vol. 45(1), pages 55-77, March.
- Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
- Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
- Demetrescu, Matei & Hanck, Christoph, 2012. "A simple nonstationary-volatility robust panel unit root test," Economics Letters, Elsevier, vol. 117(1), pages 10-13.
- Silverstein, J. W. & Choi, S. I., 1995. "Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 295-309, August.
- Theodoros Tsagaris & Ajay Jasra & Niall Adams, 2012. "Robust and adaptive algorithms for online portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1651-1662, November.
- Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
- Pedro Duarte Silva, A., 2011. "Two-group classification with high-dimensional correlated data: A factor model approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2975-2990, November.
- Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
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