Estimation of the average number of continuous crossings for non-stationary non-diffusion processes
AZAÏS, Romain
Simulation et Analyse de la morphogenèse in siliCo [MOSAIC]
Reproduction et développement des plantes [RDP]
Simulation et Analyse de la morphogenèse in siliCo [MOSAIC]
Reproduction et développement des plantes [RDP]
GENADOT, Alexandre
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
AZAÏS, Romain
Simulation et Analyse de la morphogenèse in siliCo [MOSAIC]
Reproduction et développement des plantes [RDP]
Simulation et Analyse de la morphogenèse in siliCo [MOSAIC]
Reproduction et développement des plantes [RDP]
GENADOT, Alexandre
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
Article de revue
Ce document a été publié dans
Journal of Statistical Planning and Inference. 2019-01, vol. 198, p. 119-138
Elsevier
Résumé en anglais
Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (in dimension d = 1) or hypersurface (in ...Lire la suite >
Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (in dimension d = 1) or hypersurface (in dimension d ≥ 2). Of course, you can actually estimate this quantity by its empirical version counting the number of observed crossings. But is there a better way? In this paper, for a wide class of piecewise smooth processes, we propose estimators of the average number of continuous crossings of an hypersurface based on Kac-Rice formulae. We revisit these formulae in the uni-and multivariate framework in order to be able to handle non-stationary processes. Our statistical method is tested on both simulated and real data.< Réduire
Mots clés en anglais
Average number of crossings
Piecewise deterministic process
Plug-in estimators
Origine
Importé de halUnités de recherche