Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/214187
Authors: 
Ledoit, Olivier
Wolf, Michael
Year of Publication: 
2020
Series/Report no.: 
Working Paper 327
Abstract: 
Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is to be minimized. We solve the problem of optimal covariance matrix estimation under a variety of loss functions motivated by statistical precedent, probability theory, and differential geometry. A key ingredient of our nonlinear shrinkage methodology is a new estimator of the angle between sample and population eigenvectors, without making strong assumptions on the population eigenvalues. We also introduce a broad family of covariance matrix estimators that can handle all regular functional transformations of the population covariance matrix under large-dimensional asymptotics. In addition, we compare via Monte Carlo simulations our methodology to two simpler ones from the literature, linear shrinkage and shrinkage based on the spiked covariance model.
Subjects: 
large-dimensional asymptotics
random matrix theory
rotation equivariance
JEL: 
C13
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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