Arbeitspapier
Direct nonlinear shrinkage estimation of large-dimensional covariance matrices
This paper introduces a nonlinear shrinkage estimator of the covariance matrix that does not require recovering the population eigenvalues first. We estimate the sample spectral density and its Hilbert transform directly by smoothing the sample eigenvalues with a variable-bandwidth kernel. Relative to numerically inverting the so-called QuEST function, the main advantages of direct kernel estimation are: (1) it is much easier to comprehend because it is analogous to kernel density estimation; (2) it is only twenty lines of code in Matlab - as opposed to thousands - which makes it more verifiable and customizable; (3) it is 200 times faster without significant loss of accuracy; and (4) it can handle matrices of a dimension larger by a factor of ten. Even for dimension 10,000, the code runs in less than two minutes on a desktop computer; this makes the power of nonlinear shrinkage as accessible to applied statisticians as the one of linear shrinkage.
- Language
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Englisch
- Bibliographic citation
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Series: Working Paper ; No. 264
- Classification
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Wirtschaft
Estimation: General
- Subject
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Kernel estimation
Hilbert transform
large-dimensional asymptotics
nonlinear shrinkage
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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2017
- DOI
-
doi:10.5167/uzh-139880
- Handle
- Last update
-
10.03.2025, 11:42 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
- 2017
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