Bernstein-type inequality for a class of dependent random matrices

Marwa Banna; Florence Merlevède; Pierre Youssef

doi:10.1142/S2010326316500064

Bernstein-type inequality for a class of dependent random matrices

Marwa Banna, Florence Merlevède, Pierre Youssef

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	1650006
Journal	Random Matrices: Theory and Application
Volume	5
Issue number	2
DOIs	https://doi.org/10.1142/S2010326316500064
State	Published - Apr 1 2016

Keywords

Bernstein inequality
Random matrices
absolute regularity
deviation inequality
β -mixing coefficients

ASJC Scopus subject areas

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

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10.1142/S2010326316500064

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AU - Banna, Marwa

AU - Merlevède, Florence

AU - Youssef, Pierre

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N2 - 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.

AB - 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.

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KW - β -mixing coefficients

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Bernstein-type inequality for a class of dependent random matrices

Abstract

Keywords

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