Functional CLT for sample covariance matrices

Bai, Zhidong ; Wang, Xiaoying ; Zhou, Wang

Bernoulli, Tome 16 (2010) no. 1, p. 1086-1113 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2010-11-15
Classification:  Bernstein polynomial,  central limit theorem,  sample covariance matrices,  Stieltjes transform