Asymptotics of empirical eigen-structure for high dimensional sample covariance matrices of general form

Xiucai Ding

Published 2017-08-21Version 1

In this paper, we study the local asymptotics of the eigenvalues and eigenvectors for a general class of sample covariance matrices, where the spectrum of the population covariance matrices can have a finite number of spikes and bulk components. Our paper is a unified framework combining the spiked model and covariance matrices without outliers. Examples and statistical applications are considered to illustrate our results.