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hal-00584933, version 2

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

Damien Passemier (Author to contact preferably) 1, Jian-Feng Yao () 2

Random Matrices. Theory and Applications 1, 1 (2012) 19 p.

Abstract: 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.

  • 1:  Institut de Recherche Mathématique de Rennes (IRMAR)
  • CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
  • 2:  Department of Statistics and Actuarial Science [University of Hong Kong] (DSAS)
  • University of Hong Kong
  • Domain : Mathematics/Statistics
    Statistics/Statistics Theory
  • Keywords : Spiked population model – High-dimensional statistics – Sample covariance matrices – Factor model – Extreme eigenvalues – Tracy-Widom laws
  • Internal note : 11-17
  • Available versions :  v1 (2011-04-12) v2 (2011-04-14)
 
  • hal-00584933, version 2
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  • From: Damien Passemier <>
  • Submitted on: Wednesday, 13 April 2011 13:33:00
  • Updated on: Monday, 14 January 2013 17:14:57