Asymptotic normality for eigenvalue statistics of a general sample covariance matrix when p/n→∞ and applications
Jiaxin Qiu, Zeng Li, Jianfeng Yao
The Annals of Statistics · 2023 · Volume 51 · Issue 3
Abstract
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultrahigh-dimensional setting, that is, when the dimension to sample size ratio p/n→∞. Based on this CLT result, we extend the covariance matrix test problem to the new ultra-high-dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the general asymptotic normality of eigenvalue statistics, as well as the two developed tests.
Keywords
62H10, 62H15, asymptotic normality, general sample covariance matrix, Linear spectral statistics, matrix white noise, separable covariance, ultra-dimension
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