Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models

Wang Qinwen (Zhejiang University)
Su Zhonggen (Zhejiang University)
Yao Jianfeng (The University of Hong Kong)

Abstract


In this paper, we derive a joint central limit theorem  for random vector whose components are function of random sesquilinear forms. This result is a natural extension of the existing central limit theory on random quadratic forms. We also provide  applications in random matrix theory related to large-dimensional spiked population models. For the first application, we  find the joint distribution of grouped   extreme sample eigenvalues correspond to the spikes. And for the second application, under the assumption that the population covariance matrix is diagonal with $k$ (fixed) simple spikes, we derive  the asymptotic joint distribution of the extreme sample eigenvalue and its corresponding sample eigenvector projection.

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Pages: 1-28

Publication Date: October 30, 2014

DOI: 10.1214/EJP.v19-3339

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