The tracy-widom limit for the largest eigenvalues of singular complex wishart matrices

• 成果类型: Article
• 署名作者: Onatski, Alexei
• 署名单位: Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP454
• 发表日期: 2008
• 页码: 470-490
• 关键词: sample covariance matrices; spacing distributions; number; arbitrage; models

摘要

This paper extends the work of E1 Karoui [Ann. Probab. 35 (2007) 663-714] which finds the Tracy-Widom limit for the largest eigenvalue of a nonsingular p-dimensional complex Wishart matrix WC (Omega(p), n) to the case of several of the largest eigenvalues of the possibly singular (n < p) matrix WC(Omega(p), n). As a byproduct, we extend all results of Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643-1697] to the singular Wishart matrix case. We apply our findings to obtain a 95% confidence set for the number of common risk factors in excess stock returns.