The largest eigenvalues of sample covariance matrices for a spiked population: diagonal case.
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Document de travail - Pré-publication
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
sample covariance matrices from a spiked population
universality of the fluctuations of the largest eigenvalues
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