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 (nℂ(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.
Publié le : 2008-04-15
Classification:
Singular Wishart matrix,
Tracy–Widom distribution,
largest eigenvalues,
random matrix theory,
approximate factor model,
number of factors,
arbitrage pricing theory,
60F05,
62E20
@article{1206018194,
author = {Onatski, Alexei},
title = {The Tracy--Widom limit for the largest eigenvalues of singular complex Wishart matrices},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 470-490},
language = {en},
url = {http://dml.mathdoc.fr/item/1206018194}
}
Onatski, Alexei. The Tracy–Widom limit for the largest eigenvalues of singular complex Wishart matrices. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 470-490. http://gdmltest.u-ga.fr/item/1206018194/