@article{EJP3339,
author = {Wang Qinwen and Su Zhonggen and Yao Jianfeng},
title = {Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Central limit theorem; Extreme eigenvalues; Extreme eigenvectors; Joint distribution; Large-dimensional sample covariance matrices; Random quadratic form; Random sesqulinear form; Spiked population model},
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.},
pages = {no. 103, 1-28},
issn = {1083-6489},
doi = {10.1214/EJP.v19-3339},
url = {http://ejp.ejpecp.org/article/view/3339}}