# Numerical implementation of the QuEST function

*Olivier Ledoit* and
*Michael Wolf*

*Computational Statistics & Data Analysis*, 2017, vol. 115, issue C, 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.

**Keywords:** Large-dimensional asymptotics; Numerical optimization; Random Matrix Theory; Spectrum estimation (search for similar items in EconPapers)

**Date:** 2017

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**Citations:** View citations in EconPapers (13)

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Working Paper: Numerical implementation of the QuEST function (2017)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:csdana:v:115:y:2017:i:c:p:199-223

**DOI:** 10.1016/j.csda.2017.06.004

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