%0 Journal Article
%T The Tracy--Widom limit for the largest eigenvalues of singular complex Wishart matrices
%A Alexei Onatski
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/07-AAP454
%X This paper extends the work of El 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 $W_{\mathbb{C}}(\Omega_p,n)$ to the case of several of the largest eigenvalues of the possibly singular $(n<p)$ matrix $W_{\mathbb{C}}(\Omega_p,n).$ 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.
%U http://arxiv.org/abs/0803.4155v1