The largest eigenvalues of sample covariance matrices for a spiked population: diagonal case.

Delphine Féral (1) , Sandrine Péché (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IF - Institut Fourier

We consider large complex random sample covariance matrices obtained from ``spiked populations'', that is when the true covariance matrix is diagonal with all but finitely many eigenvalues equal to one. We investigate the limiting behavior of the largest eigenvalues when the population and the sample sizes both become large. Under some conditions on moments of the sample distribution, we prove that the asymptotic fluctuations of the largest eigenvalues are the same as for a complex Gaussian sample with the same true covariance. The real setting is also considered.

Mots clés: sample covariance matrices from a spiked population; universality of the fluctuations of the largest eigenvalues

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Probabilités [math.PR]

Delphine Féral, Sandrine Péché. The largest eigenvalues of sample covariance matrices for a spiked population: diagonal case.. 2008. ⟨hal-00346619⟩