Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527226 | Stochastic Processes and their Applications | 2014 | 33 Pages |
Abstract
We study the joint limit distribution of the k largest eigenvalues of a pÃp sample covariance matrix XXT based on a large pÃn matrix X. The rows of X are given by independent copies of a linear process, Xit=âjcjZi,tâj, with regularly varying noise (Zit) with tail index αâ(0,4). It is shown that a point process based on the eigenvalues of XXT converges, as nââ and pââ at a suitable rate, in distribution to a Poisson point process with an intensity measure depending on α and âcj2. This result is extended to random coefficient models where the coefficients of the linear processes (Xit) are given by cj(θi), for some ergodic sequence (θi), and thus vary in each row of X. As a by-product of our techniques we obtain a proof of the corresponding result for matrices with iid entries in cases where p/n goes to zero or infinity and αâ(0,2).
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Richard A. Davis, Oliver Pfaffel, Robert Stelzer,