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 Marčenko–Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.
Citation
Zhidong Bai. Xiaoying Wang. Wang Zhou. "Functional CLT for sample covariance matrices." Bernoulli 16 (4) 1086 - 1113, November 2010. https://doi.org/10.3150/10-BEJ250
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