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Type | Working Paper |
Scope | Discipline-based scholarship |
Title | Numerical implementation of the QuEST function |
Organization Unit | |
Authors |
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Language |
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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. |
Official URL | http://www.econ.uzh.ch/static/wp/econwp215.pdf |
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PDF File | Download from ZORA |
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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 |