Estimation non-param\'etrique de la densit\'e spectrale d'un processus gaussien \'echantillonn\'e al\'eatoirement
Statistics Theory
2008-07-03 v1 Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0802.1388,
title = {Estimation non-param\'etrique de la densit\'e spectrale d'un processus gaussien \'echantillonn\'e al\'eatoirement},
author = {Jean-Marc Bardet and Pierre Bertrand and Véronique Billat},
journal= {arXiv preprint arXiv:0802.1388},
year = {2008}
}