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Direct Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices


Ledoit, Olivier; Wolf, Michael (2017). Direct Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices. Working paper series / Department of Economics 264, University of Zurich.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C13
Uncontrolled Keywords:Kernel estimation, Hilbert transform, large-dimensional asymptotics, nonlinear shrinkage, rotation equivariance
Language:English
Date:September 2017
Deposited On:03 Oct 2017 14:54
Last Modified:03 Oct 2017 15:01
Series Name:Working paper series / Department of Economics
Number of Pages:45
ISSN:1664-7041
Official URL:http://www.econ.uzh.ch/static/wp/econwp264.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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