Arbeitspapier
Shrinkage estimation of large covariance matrices: Keep it simple, statistician?
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.
- Language
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Englisch
- Bibliographic citation
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Series: Working Paper ; No. 327
- Classification
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Wirtschaft
Estimation: General
- Subject
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large-dimensional asymptotics
random matrix theory
rotation equivariance
- Event
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Geistige Schöpfung
- (who)
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Ledoit, Olivier
Wolf, Michael
- Event
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Veröffentlichung
- (who)
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University of Zurich, Department of Economics
- (where)
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Zurich
- (when)
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2020
- DOI
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doi:10.5167/uzh-172202
- Handle
- Last update
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10.03.2025, 11:44 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Ledoit, Olivier
- Wolf, Michael
- University of Zurich, Department of Economics
Time of origin
- 2020
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Shrinkage estimation of large covariance matrices: Keep it simple, statistician?
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Güterbeschreibung Nr. 285
Shrinkage estimation of large covariance matrices: Keep it simple, statistician?
Shrinkage estimation of large covariance matrices: Keep it simple, statistician?
Quadratic shrinkage for large covariance matrices
Quadratic shrinkage for large covariance matrices
Direct nonlinear shrinkage estimation of large-dimensional covariance matrices
Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks
Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks
Large dynamic covariance matrices
Optimal estimation of a large-dimensional covariance matrix under Stein's loss
Optimal estimation of a large-dimensional covariance matrix under Stein's loss
Optimal estimation of a large-dimensional covariance matrix under Stein's loss