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


 
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1. Title Title of document Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models
 
2. Creator Author's name, affiliation, country Wang Qinwen; Zhejiang University; China
 
2. Creator Author's name, affiliation, country Su Zhonggen; Zhejiang University; China
 
2. Creator Author's name, affiliation, country Yao Jianfeng; The University of Hong Kong; Hong Kong
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Central limit theorem; Extreme eigenvalues; Extreme eigenvectors; Joint distribution; Large-dimensional sample covariance matrices; Random quadratic form; Random sesqulinear form; Spiked population model
 
3. Subject Subject classification Primary 60F05; secondary 60B20
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-10-30
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3339
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3339
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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