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Contribution Details

Type Working Paper
Scope Discipline-based scholarship
Title Numerical implementation of the QuEST function
Organization Unit
  • Olivier Ledoit
  • Michael Wolf
  • English
Institution University of Zurich
Series Name Working paper series / Department of Economics
Number 215
ISSN 1664-7041
Number of Pages 42
Date 2017
Abstract Text 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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Keywords Large-dimensional asymptotics, numerical optimization, random matrix theory, spectrum estimation, Optimierungsproblem, Matrizentheorie, Algorithmus, Monte-Carlo-Simulation
Additional Information Revised version