2003 Prépublication d'Orsay numéro 2003-51 (16/09/2003)



EFFICIENT SEMI-PARAMETRIC ESTIMATION OF THE PERIODS IN A SUPERPOSITION OF PERIODIC FUNCTIONS WITH UNKNOWN SHAPE.

GASSIAT, Elisabeth - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex
LEVY-LEDUC, Céline - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex


Mots Clés : Periodic functions; Semi-parametric estimation; Efficiency

Classification MSC : 62G20 ; 62N02.


Resumé :

Abstract :
We consider the estimation of the periods in a sum of periodic functions of unknown shape corrupted by white noise. In the case of a single periodic signal, we propose a consistent and asymptotically efficient semi-parametric estimator of the period. In this case, the asymptotic variance of the estimation of the period is four times as big as it would be if the function was of known shape. We then study the case of a sum of two periodic signals of unknown shape with different periods. For a large class of signals, we propose semi-parametric estimators of the two periods that are consistent and asymptotically gaussian. When the ratio of the periods is not rational, the estimators are asymptotically independent and efficient.

Article : Fichier Postscript
Contact : Celine.Levy-Leduc@math.u-psud.fr