Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions

Olivier Ledoit and Michael Wolf

Journal of Multivariate Analysis, 2015, vol. 139, issue C, 360-384

Abstract: 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.

Keywords: Large-dimensional asymptotics; Covariance matrix eigenvalues; Nonlinear shrinkage; Principal component analysis (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (47)

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Working Paper: Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions (2013)
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DOI: 10.1016/j.jmva.2015.04.006

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