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Numerical implementation of the QuEST function


Ledoit, Olivier; Wolf, Michael (2017). Numerical implementation of the QuEST function. Computational Statistics & Data Analysis, 115:199-223.

Abstract

Certain estimation problems involving the covariance matrix in large dimensions are considered. 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, an estimator of the eigenvalues of the population covariance matrix has been proposed that is consistent according to a mean-squared criterion under large-dimensional asymptotics. It requires numerical inversion of a multivariate nonrandom function called the QuEST function. The numerical implementation of this QuEST function in practice is explained through a series of six successive steps. An algorithm is provided in order to compute the Jacobian of the QuEST function analytically, which is necessary for numerical inversion via a nonlinear optimizer. Monte Carlo simulations document the effectiveness of the code.

Abstract

Certain estimation problems involving the covariance matrix in large dimensions are considered. 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, an estimator of the eigenvalues of the population covariance matrix has been proposed that is consistent according to a mean-squared criterion under large-dimensional asymptotics. It requires numerical inversion of a multivariate nonrandom function called the QuEST function. The numerical implementation of this QuEST function in practice is explained through a series of six successive steps. An algorithm is provided in order to compute the Jacobian of the QuEST function analytically, which is necessary for numerical inversion via a nonlinear optimizer. Monte Carlo simulations document the effectiveness of the code.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > Computational Mathematics
Physical Sciences > Computational Theory and Mathematics
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Large-dimensional asymptotics, numerical optimization, Random Matrix Theory, spectrum estimation
Language:English
Date:November 2017
Deposited On:18 Jan 2018 13:42
Last Modified:28 Jul 2020 12:50
Publisher:Elsevier
ISSN:0167-9473
Additional Information:Also published as Department of Economics, Working Paper No. 215 (see https://doi.org/10.5167/uzh-120492).
OA Status:Green
Publisher DOI:https://doi.org/10.1016/j.csda.2017.06.004

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