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

被引：34

作者：

Onatski, Alexei ^{[1
]}

机构：

[1] Columbia Univ, Dept Econ, New York, NY 10027 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2008年 / 18卷 / 02期

关键词：

singular Wishart matrix; Tracy-Widom distribution; largest eigenvalues; random matrix theory; approximate factor model; number of factors; arbitrage pricing theory;

D O I：

10.1214/07-AAP454

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：470 / 490

页数：21

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