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

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

2008-02-11

arxiv.org/abs/0802.1388v1

Annales I.S.U.P. (2008) 1-12

Mathematics

Statistics Theory

Scientific paper

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.

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