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.Comment: 35 pages, 8 figure
