Coherence of high-dimensional random matrices in a Gaussian case : application of the Chen-Stein method

Abstract

This paper studies the $\tau$-coherence of a (n x p)-observation matrix in a Gaussian framework. The $\tau$-coherence is defined as the largest magnitude outside a diagonal bandwith of size $\tau$ of the empirical correlation coefficients associated to our observations. Using the Chen-Stein method we derive the limiting law of the normalized coherence and show the convergence towards a Gumbel distribution. We generalize here the results of Cai and Jiang [CJ11a]. We assume that the covariance matrix of the model is bandwise. Moreover, we provide numerical considerations highlighting issues from the high dimension hypotheses. We numerically illustrate the asymptotic behaviour of the coherence with Monte-Carlo experiment using a HPC splitting strategy for high dimensional correlation matrices.

References in corpus (3)

• The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization
• Some strong limit theorems for the largest entries of sample correlation matrices
• Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices