Functional CLT for sample covariance matrices

Abstract

Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including $[(1-\sqrt{y}{)}^2,(1+\sqrt{y}{)}^2]$, the support of the Marucenko--Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.

Published in at http://dx.doi.org/10.3150/10-BEJ250 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries

Cited by in corpus (8)

• Gaussian fluctuations for linear spectral statistics of large random covariance matrices
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model
• Beyond universality in random matrix theory
• On Identity Tests for High Dimensional Data Using RMT
• Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices
• Joint CLT for top eigenvalues of sample covariance matrices of separable high dimensional long memory processes
• CLT for linear eigenvalue statistics for a tensor product version of sample covariance matrices
• CLT for LSS of sample covariance matrices with unbounded dispersions