swMATH ID: 38788
Software Authors: Ledoit, Olivier; Wolf, Michael
Description: Numerical implementation of the quest function. 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.
Homepage: https://arxiv.org/abs/1601.05870
Dependencies: Matlab
Keywords: large-dimensional asymptotics; numerical optimization; random matrix theory; spectrum estimation
Related Software: OptShrink; SPECTRODE; RMTool; CVXOPT; spcov; Manopt; glasso
Cited in: 11 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Numerical implementation of the QuEST function. Zbl 1466.62127
Ledoit, Olivier; Wolf, Michael

Citations by Year