Functional CLT for sample covariance matrices. (English) Zbl 1210.60025

Summary: 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 Marčenko-Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.


60F05 Central limit and other weak theorems
60B20 Random matrices (probabilistic aspects)
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