Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/162418
Authors: 
Ledoit, Olivier
Wolf, Michael
Year of Publication: 
2017
Series/Report no.: 
Working Paper Series, University of Zurich, Department of Economics 215
Abstract: 
This paper deals with certain estimation problems involving the covariance matrix in large dimensions. Due to the breakdown of finite-dimensional asymptotic theory when the dimension is not negligible with respect to the sample size, it is necessary to resort to an alternative framework known as large-dimensional asymptotics. Recently, Ledoit and Wolf (2015) have proposed an estimator of the eigenvalues of the population covariance matrix that is consistent according to a mean-square criterion under large-dimensional asymptotics. It requires numerical inversion of a multivariate nonrandom function which they call the QuEST function. The present paper explains how to numerically implement the QuEST function in practice through a series of six successive steps. It also provides an algorithm to compute the Jacobian analytically, which is necessary for numerical inversion by a nonlinear optimizer. Monte Carlo simulations document the effectiveness of the code.
Subjects: 
Large-dimensional asymptotics
numerical optimization
random matrix theory
spectrum estimation
JEL: 
C13
C61
C87
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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