Bernstein-type inequality for a class of dependent random matrices

Author:

Banna Marwa1,Merlevède Florence1,Youssef Pierre2

Affiliation:

1. Université Paris-Est, UPEM, LAMA, CNRS, UPEC, 5 Boulevard Descartes, 77 454 Marne La Vallée, France

2. Department of Mathematical and Statistical Sciences, University of Alberta, Canada

Abstract

In this paper, we obtain a Bernstein-type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix setting of the Bernstein-type inequality obtained by Merlevède et al. [Bernstein inequality and moderate deviations under strong mixing conditions, in High Dimensional Probability V: The Luminy Volume, Institute of Mathematical Statistics Collection, Vol. 5 (Institute of Mathematical Statistics, Beachwood, OH, 2009), pp. 273–292.] in the context of real-valued bounded random variables that are geometrically absolutely regular. The proofs rely on decoupling the Laplace transform of a sum on a Cantor-like set of random matrices.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory

Reference15 articles.

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