Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models

Jianfeng Yao (1) , Romain Couillet (2) , Jamal Najim (1) , Merouane Debbah (3)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 SSEC - Chaire Sciences des Systèmes et Défis Energétiques EDF/ECP/Supélec
3 Chaire Radio Flexible - Chaire Radio Flexible Alcatel-Lucent/Supélec

This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of available observations is known and comparable in magnitude to the observation dimension. An exact expression as well as an empirical, asymptotically accurate, approximation of the limiting variance is derived. Simulations are performed that corroborate the theoretical claims. A specific application to wireless sensor networks is developed.

Mots clés: population matrix estimation; large random matrices; wireless communication

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Jianfeng Yao, Romain Couillet, Jamal Najim, Merouane Debbah. Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models. IEEE Transactions on Information Theory, 2013, 59 (2), pp.1149-1163. ⟨10.1109/TIT.2012.2222862⟩. ⟨hal-00617114⟩