Numerical implementation of the QuEST function

Olivier Ledoit and Michael Wolf

No 215, ECON - Working Papers from Department of Economics - 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.

Keywords: Large-dimensional asymptotics; numerical optimization; random matrix theory; spectrum estimation (search for similar items in EconPapers)
JEL-codes: C13 C61 C87 (search for similar items in EconPapers)
Date: 2016-01, Revised 2017-01
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Related works:
Journal Article: Numerical implementation of the QuEST function (2017)
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