Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/173422
Authors: 
Ledoit, Olivier
Wolf, Michael
Year of Publication: 
2017
Series/Report no.: 
Working Paper 264
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.
Subjects: 
Kernel estimation
Hilbert transform
large-dimensional asymptotics
nonlinear shrinkage
rotation equivariance
JEL: 
C13
Persistent Identifier of the first edition: 
Document Type: 
Working Paper
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