On the empirical spectral distribution for matrices with long memory and independent rows

F. Merlevède and M. Peligrad

Stochastic Processes and their Applications, 2016, vol. 126, issue 9, 2734-2760

Abstract: In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent samples of a stationary regular sequence has a limiting distribution depending only on the spectral density of the sequence. We characterize this limit in terms of Stieltjes transform via a certain simple equation. No rate of convergence to zero of the covariances is imposed, so, the underlying process can exhibit long memory. If the stationary sequence has trivial left sigma field the result holds without any other additional assumptions. This is always true if the entries are functions of i.i.d.

Keywords: Random matrices; Stieltjes transform; Martingale approximation; Lindeberg method; Empirical eigenvalue distribution; Spectral density; Sample covariance matrix (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:9:p:2734-2760

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DOI: 10.1016/j.spa.2016.02.016

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