Header

UZH-Logo

Maintenance Infos

Analytical nonlinear shrinkage of large-dimensional covariance matrices


Ledoit, Olivier; Wolf, Michael (2018). Analytical nonlinear shrinkage of large-dimensional covariance matrices. Working paper series / Department of Economics 264, University of Zurich.

Abstract

This paper establishes the first analytical formula for optimal nonlinear shrinkage of large-dimensional covariance matrices. We achieve this by identifying and mathematically exploiting a deep connection between nonlinear shrinkage and nonparametric estimation of the Hilbert transform of the sample spectral density. Previous nonlinear shrinkage methods were numerical: QuEST requires numerical inversion of a complex equation from random matrix theory whereas NERCOME is based on a sample-splitting scheme. The new analytical approach is more elegant and also has more potential to accommodate future variations or extensions. Immediate benefits are that it is typically 1,000 times faster with the same accuracy, and accommodates covariance matrices of dimension up to 10, 000. The difficult case where the matrix dimension exceeds the sample size is also covered.

Abstract

This paper establishes the first analytical formula for optimal nonlinear shrinkage of large-dimensional covariance matrices. We achieve this by identifying and mathematically exploiting a deep connection between nonlinear shrinkage and nonparametric estimation of the Hilbert transform of the sample spectral density. Previous nonlinear shrinkage methods were numerical: QuEST requires numerical inversion of a complex equation from random matrix theory whereas NERCOME is based on a sample-splitting scheme. The new analytical approach is more elegant and also has more potential to accommodate future variations or extensions. Immediate benefits are that it is typically 1,000 times faster with the same accuracy, and accommodates covariance matrices of dimension up to 10, 000. The difficult case where the matrix dimension exceeds the sample size is also covered.

Statistics

Downloads

63 downloads since deposited on 03 Oct 2017
40 downloads since 12 months
Detailed statistics

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:November 2018
Deposited On:03 Oct 2017 14:54
Last Modified:12 Nov 2018 16:07
Series Name:Working paper series / Department of Economics
Number of Pages:55
ISSN:1664-7041
Additional Information:Revised version ; Former title: Direct Nonlinear Shrinkage Estimation of Large-Dimensional Covariance Matrices
OA Status:Green
Official URL:http://www.econ.uzh.ch/static/workingpapers.php?id=943

Download

Content: Published Version
Filetype: PDF (Version September 2017) - Registered users only
Size: 556kB
Download PDF  'Analytical nonlinear shrinkage of large-dimensional covariance matrices'.
Preview
Content: Updated Version
Filetype: PDF (Revised version November 2018)
Size: 778kB