# Asymptotic normality for eigenvalue statistics of a general sample covariance matrix when p/n → ∞ and applications

arXiv: https://arxiv.org/abs/2109.06701 · HTML: https://mlsanity.com/paper/2109.06701/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks](https://mlsanity.com/paper/2109.09304/) (2021)

## Abstract (arXiv)

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 → ∞. 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.