Estimation non-paramétrique de la densité spectrale d'un processus gaussien échantillonné aléatoirement

Jean-Marc Bardet (1, 2) , Pierre, Raphael Bertrand (3) , Véronique Billat (4)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 PAS
4 LEPHE - Laboratoire d'Etude de la PHysiologie de l'Exercice

From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual Central Limit Theorem (CLT) and an estimation of the Mean Integrate Square Error (MISE) are established. Next, to fit the applications, one considers the case where one observes a path at random times. One built a second estimator obtained by replacing the wavelet coefficients by their discretizations. A second CLT and the corresponding estimation of the MISE are provided. Finally, simulation results and an application on the heartbeat time series of marathon runners are presented.

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Jean-Marc Bardet, Pierre, Raphael Bertrand, Véronique Billat. Estimation non-paramétrique de la densité spectrale d'un processus gaussien échantillonné aléatoirement. Annales de l'ISUP, 2008, LII (1-2), pp.123-138. ⟨hal-00250150⟩