Asymptotic normality for eigenvalue statistics of a general sample covariance matrix when $p/n\to \infty$ and applications

Abstract

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n\to \infty$. Based on this CLT result, we first adapt the covariance matrix test problem to the new ultra-high dimensional context. Then as a second application, we develop a new test for the separable covariance structure of 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 second test for separable covariance structure of matrix-valued white noise.

References in corpus (4)

• On Asymptotic Properties of Large Random Matrices with Independent Entries
• On the sphericity test with large-dimensional observations
• Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero
• CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

Cited by in corpus (1)

• Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks