Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/77592
Authors: 
Ledoit, Olivier
Wolf, Michael
Year of Publication: 
2013
Series/Report no.: 
Working Paper Series, Department of Economics, University of Zurich 122
Abstract: 
This paper revisits the methodology of Stein (1975, 1986) for estimating a covariance matrix in the setting where the number of variables can be of the same magnitude as the sample size. Stein proposed to keep the eigenvectors of the sample covariance matrix but to shrink the eigenvalues. By minimizing an unbiased estimator of risk, Stein derived an 'optimal' shrinkage transformation. Unfortunately, the resulting estimator has two pitfalls: the shrinkage transformation can change the ordering of the eigenvalues and even make some of them negative. Stein suggested an ad hoc isotonizing algorithm that post-processes the transformed eigenvalues and thereby fixes these problems. We offer an alternative solution by minimizing the limiting expression of the unbiased estimator of risk under large-dimensional asymptotics, rather than the finite-sample expression. Compared to the isotonized version of Stein's estimator, our solution is theoretically more elegant and also delivers improved performance, as evidenced by Monte Carlo simulations.
Subjects: 
large-dimensional asymptotics
nonlinear shrinkage estimation
random matrix theory
rotation equivariance
Stein's loss
JEL: 
C13
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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