Numerical Implementation of the QuEST Function

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 lar...

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Bibliographic Details
Published inarXiv.org
Main Authors Ledoit, Olivier, Wolf, Michael
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.01.2016
Subjects
Algorithms
Asymptotic properties
Computer simulation
Covariance matrix
Economic models
Eigenvalues
Monte Carlo simulation
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Summary: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.
ISSN:2331-8422