Functional CLT for sample covariance matrices

Details Functional CLT for sample covariance matrices Functional CLT for sample covariance matrices

2010-11-26

arxiv.org/abs/1011.5729v1

Bernoulli 2010, Vol. 16, No. 4, 1086-1113

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ250 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ250

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 Mar\u{c}enko--Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.

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