Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/77590 
Year of Publication: 
2013
Series/Report no.: 
Working Paper No. 105
Publisher: 
University of Zurich, Department of Economics, Zurich
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 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.
Subjects: 
large-dimensional asymptotics
covariance matrix eigenvalues
nonlinear shrinkage
principal component analysis
JEL: 
C13
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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