On the behavior of large empirical autocovariance matrices between the past and the future-Reference-Cited by-同舟云学术

On the behavior of large empirical autocovariance matrices between the past and the future

Published:2020-07-28 Issue:02 Volume:10 Page:2150021
ISSN:2010-3263
Container-title:Random Matrices: Theory and Applications
language:en
Short-container-title:Random Matrices: Theory Appl.

Author:

Loubaton P.¹^ORCID,Tieplova D.¹²

Affiliation:

1. Laboratoire d’Informatique Gaspard Monge, UMR 8049, Université Paris-Est Marne la Vallée, 5 Bd. Descartes, Cite Descartes, 77454 Marne la Vallée Cedex 2, France

2. Department of Theoretical Physics, Institute for Low Temperature Physics and Engineering, 47 Nauky Ave., Kharkiv 61103, Ukraine

Abstract

The asymptotic behavior of the distribution of the squared singular values of the sample autocovariance matrix between the past and the future of a high-dimensional complex Gaussian uncorrelated sequence is studied. Using Gaussian tools, it is established that the distribution behaves as a deterministic probability measure whose support [Formula: see text] is characterized. It is also established that the squared singular values are almost surely located in a neighborhood of [Formula: see text].

Funder

Agence Nationale de la Recherche, Bézout Labex

Agence Nationale de la Recherche

Publisher

World Scientific Pub Co Pte Lt

Subject

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

Link

https://www.worldscientific.com/doi/pdf/10.1142/S2010326321500210

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