Asymptotic normality of sample covariance matrix for mixed spectra time series: Application to sinusoidal frequencies estimation

Jean-Pierre Delmas (1, 2)

1 TSP - CITI - Communications, Images et Traitement de l'Information
2 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications

This correspondence addresses the asymptotic normal distribution of the sample mean and the sample covariance matrix of mixed spectra time series containing a sum of sinusoids and a moving average process. Two central limit theorems are proved. As an application of this result, the asymptotic normal distribution of any sinusoidal frequencies estimator of such time series based on second-order statistics is deduced.

Mots clés: central limit theorem; sample covariance matrix; mixed spectra time series; covariancebased sinusoidal frequencies estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Traitement du signal et de l'image [eess.SP]

Jean-Pierre Delmas. Asymptotic normality of sample covariance matrix for mixed spectra time series: Application to sinusoidal frequencies estimation. IEEE Transactions on Information Theory, 2001. ⟨hal-03399917⟩