Limiting Spectral Distribution of Circulant Type Matrices with Dependent Inputs

Arup Bose (Indian Statistical Institute Kolkata)
Rajat Subhra Hazra (Indian Statistical Institute Kolkata)
Koushik Saha (Indian Statistical Institute Kolkata)

Abstract


Limiting spectral distribution (LSD) of scaled eigenvalues of circulant, symmetric circulant and a class of k-circulant matrices are known when the input sequence is independent and identically distributed with finite moments of suitable order. We derive the LSD of these matrices when the input sequence is a stationary, two sided moving average process of infinite order. The limits are suitable mixtures of normal, symmetric square root of the chisquare, and other mixture distributions, with the spectral density of the process involved in the mixtures.

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Pages: 2463-2491

Publication Date: November 9, 2009

DOI: 10.1214/EJP.v14-714

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