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Analytical nonlinear shrinkage of large-dimensional covariance matrices

Olivier Ledoit and Michael Wolf ()

No 264, ECON - Working Papers from Department of Economics - 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.

Keywords: Kernel estimation; Hilbert transform; large-dimensional asymptotics; nonlinear shrinkage; rotation equivariance (search for similar items in EconPapers)
JEL-codes: C13 (search for similar items in EconPapers)
Date: 2017-09, Revised 2018-11
New Economics Papers: this item is included in nep-ecm
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