The eigenvector LSD of information plus noise matrices and its application to linear regression model

Abstract

In this paper, we investigate the limit of the eigenvector empirical spectral distribution (VESD) of large dimensional information plus noise matrices Cn=1nTn1/2(Xn+Rn)(Xn+Rn)′Tn1/2, where Xn are p×n random matrices with independent and identically distributed entries, Tn and Rn are non-random matrices. It is shown that as p/n→c∈(0,∞), the VESD of Cn has a deterministic limit under some mild conditions. The theoretical result is applied to the model selection problems in high dimensional linear regression model.