Abstract
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 Wℂ(Ωp, n) to the case of several of the largest eigenvalues of the possibly singular (n<p) matrix Wℂ(Ωp, 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.
Citation
Alexei Onatski. "The Tracy–Widom limit for the largest eigenvalues of singular complex Wishart matrices." Ann. Appl. Probab. 18 (2) 470 - 490, April 2008. https://doi.org/10.1214/07-AAP454
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