QuEST 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 1466.62127Ledoit, Olivier; Wolf, Michael 2017 all top 5 Cited by 18 Authors 4 Ledoit, Olivier 4 Wolf, Michael 1 Arizmendi, Octavio 1 Banerjee, Samprit 1 Bouchard, Florent 1 Cho, Seonghun 1 Choi, Young-Geun 1 Cordero-Grande, Lucilio 1 Couillet, Romain 1 Ding, Xiucai 1 Ginolhac, Guillaume 1 Katayama, Shota 1 Leeb, William E. 1 Lim, Johan 1 Monni, Stefano 1 Tarrago, Pierre 1 Tiomoko, Malik 1 Yang, Fan all top 5 Cited in 9 Serials 2 The Annals of Statistics 2 Computational Statistics and Data Analysis 1 Journal of Multivariate Analysis 1 Journal of Statistical Planning and Inference 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Advances in Computational Mathematics 1 Bernoulli 1 Journal of Statistical Mechanics: Theory and Experiment 1 AStA. Advances in Statistical Analysis all top 5 Cited in 10 Fields 8 Statistics (62-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 3 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year