HAL: hal-00346619, version 1

arXiv: 0812.2320

Detailed view

Export this paper BibTeX - EndNote - TEI - RefWorks -

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

Delphine Féral (  Corresponding author ) 1, Sandrine Péché 2

(2008-12-11)

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.

1:	Institut de Mathématiques de Bordeaux (IMB)
	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
2:	Institut Fourier (IF)
	CNRS : UMR5582 – Université Joseph Fourier - Grenoble I

Subject

:

Mathematics/Mathematical Physics Physics/Mathematical Physics Mathematics/Probability

Keyword(s): sample covariance matrices from a spiked population – universality of the fluctuations of the largest eigenvalues

hal-00346619, version 1

http://hal.archives-ouvertes.fr/hal-00346619

oai:hal.archives-ouvertes.fr:hal-00346619

From: Delphine Féral <>

Submitted on: Thursday, 11 December 2008 20:09:36

Updated on: Monday, 15 December 2008 14:11:13