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

2021/10/13 by Maxime Boucher, Boucher, M, Didier Chauveau +3
Mathematics · Medicine · #Advanced Algebra and Geometry #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2110.06574

openalex publication_date 2021/10/13 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

This paper studies the τ-coherence of a (n x p)-observation matrix in a Gaussian framework. The τ-coherence is defined as the largest magnitude outside a diagonal bandwith of size τ 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.

Citations

• On the distribution of the largest eigenvalue in principal components analysis
• The Chen-Stein method for Poisson functionals
• Stable signal recovery from incomplete and inaccurate measurements
• On the Distribution of the Roots of Certain Symmetric Matrices

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