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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title Shrinkage estimation of large covariance matrices: keep it simple, statistician?
Organization Unit
  • Olivier Ledoit
  • Michael Wolf
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 327
ISSN 1664-705X
Number of Pages 34
Date 2021
Abstract Text 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.
Other Identification Number merlin-id:18370
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Keywords Large-dimensional asymptotics, random matrix theory, rotation equivariance, Kovarianzfunktion, Risikomanagement, Verlust, Modellierung, Eigenwert, Monte-Carlo-Simulation
Additional Information Revised version