On determining the number of spikes in a high-dimensional spiked population model

Damien Passemier (1) , Jian-Feng Yao (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 DSAS - Department of Statistics and Actuarial Science [University of Hong Kong]

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific fields, including signal processing (linear mixture model) or economics (factor model). Several recent papers studied the asymptotic behavior of the eigenvalues of the sample covariance matrix (sample eigenvalues) when the dimension of the observations and the sample size both grow to infinity so that their ratio converges to a positive constant. Using these results, we propose a new estimator based on the difference between two consecutive sample eigenvalues.

Mots clés: Spiked population model; High-dimensional statistics; Sample covariance matrices; Factor model; Extreme eigenvalues; Tracy-Widom laws

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Damien Passemier, Jian-Feng Yao. On determining the number of spikes in a high-dimensional spiked population model. Random Matrices: Theory and Applications, 2012, 1 (1), 19 p. ⟨10.1142/S201032631150002X⟩. ⟨hal-00584933v2⟩