Local Laws for Sparse Sample Covariance Matrices

Alexander N. Tikhomirov and Dmitry A. Timushev
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Alexander N. Tikhomirov: Institute of Physics and Mathematics, Komi Science Center of Ural Branch of RAS, 167982 Syktyvkar, Russia
Dmitry A. Timushev: Institute of Physics and Mathematics, Komi Science Center of Ural Branch of RAS, 167982 Syktyvkar, Russia

Mathematics, 2022, vol. 10, issue 13, 1-38

Abstract: We proved the local Marchenko–Pastur law for sparse sample covariance matrices that corresponded to rectangular observation matrices of order n × m with n / m → y (where y > 0 ) and sparse probability n p n > log β n (where β > 0 ). The bounds of the distance between the empirical spectral distribution function of the sparse sample covariance matrices and the Marchenko–Pastur law distribution function that was obtained in the complex domain z ∈ D with Im z > v 0 > 0 (where v 0 ) were of order log 4 n / n and the domain bounds did not depend on p n while n p n > log β n .

Keywords: sparse sample covariance matrices; local Marchenko–Pastur law; Stieltjes transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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