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arXiv · 1011.5729

Functional CLT for sample covariance matrices

Zhidong Bai·Xiaoying Wang·Wang Zhou
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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.

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Zhidong Bai, Xiaoying Wang, Wang Zhou. 2010-11-26. Functional CLT for sample covariance matrices. https://doi.org/10.3150/10-bej250

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