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

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dc.creatorBardet, Jean-Marc
dc.creatorBertrand, Pierre
dc.creatorBillat, Véronique
dc.date2008-02-11
dc.date.accessioned2026-07-07T09:47:57Z
dc.date.available2026-07-07T09:47:57Z
dc.descriptionFrom 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.
dc.identifierhttps://arxiv.org/abs/0802.1388
dc.identifierhttp://arxiv.org/abs/0802.1388
dc.identifierAnnales I.S.U.P. (2008) 1-12
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164033
dc.subjectStatistics Theory
dc.titleEstimation non-paramétrique de la densité spectrale d'un processus gaussien échantillonné aléatoirement
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