Limit Theory for the largest eigenvalues of sample covariance matrices with heavy-tails
Abstract
We study the joint limit distribution of the largest eigenvalues of a sample covariance matrix based on a large matrix . The rows of are given by independent copies of a linear process, , with regularly varying noise with tail index . It is shown that a point process based on the eigenvalues of converges, as and at a suitable rate, in distribution to a Poisson point process with an intensity measure depending on and . This result is extended to random coefficient models where the coefficients of the linear processes are given by , for some ergodic sequence , and thus vary in each row of . As a by-product of our techniques we obtain a proof of the corresponding result for matrices with iid entries in cases where goes to zero or infinity and .
Keywords
Cite
@article{arxiv.1108.5464,
title = {Limit Theory for the largest eigenvalues of sample covariance matrices with heavy-tails},
author = {Richard A. Davis and Oliver Pfaffel and Robert Stelzer},
journal= {arXiv preprint arXiv:1108.5464},
year = {2012}
}
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30 pages