Limiting spectral distribution of Toeplitz and Hankel matrices with dependent entries

Shambhu Nath Maurya

Statistics & Probability Letters, 2024, vol. 209, issue C

Abstract: This article deals with the limiting spectral distributions (LSD) of symmetric Toeplitz and Hankel matrices with dependent entries. For any fixed integer m≥0, we consider these n×n matrices with entries {Yj(m)/n;j∈Z}, where Yj(m)=∑r=−mmXj+r and {Xk} are i.i.d. random variables with mean zero and variance one. We provide explicit expressions for the LSDs. As a special case (m=0), this article provides an alternate proof for the LSDs of these matrices when the entries are i.i.d. with mean zero and variance one. The method is based on the moment method.

Keywords: Toeplitz matrix; Hankel matrix; Limiting spectral distribution; Empirical spectral distribution; Moment method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110092

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