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Numerical implementation of the QuEST function


Ledoit, Olivier; Wolf, Michael (2017). Numerical implementation of the QuEST function. Working paper series / Department of Economics 215, University of Zurich.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C13, C61, C87
Uncontrolled Keywords:Large-dimensional asymptotics, numerical optimization, random matrix theory, spectrum estimation
Language:English
Date:January 2017
Deposited On:20 Jan 2016 16:04
Last Modified:17 Aug 2017 09:45
Series Name:Working paper series / Department of Economics
Number of Pages:42
ISSN:1664-7041
Additional Information:Revised version
Official URL:http://www.econ.uzh.ch/static/wp/econwp215.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers-new.php

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