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

Yuling Li, Huanchao Zhou and Jiang Hu

Statistics & Probability Letters, 2023, vol. 197, issue C

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.

Keywords: Random matrix theory; Linear regression model; ESD; LSD; Information plus noise matrix (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109811

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