Estimation of the average number of continuous crossings for non-stationary non-diffusion processes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Statistical Planning and Inference Année : 2019

Estimation of the average number of continuous crossings for non-stationary non-diffusion processes

Résumé

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.
Fichier principal
Vignette du fichier
crossings.pdf (838.75 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01499914 , version 1 (01-04-2017)
hal-01499914 , version 2 (03-11-2017)
hal-01499914 , version 3 (13-04-2018)

Identifiants

Citer

Romain Azaïs, Alexandre Genadot. Estimation of the average number of continuous crossings for non-stationary non-diffusion processes. Journal of Statistical Planning and Inference, 2019, 198, pp.119-138. ⟨10.1016/j.jspi.2018.04.002⟩. ⟨hal-01499914v3⟩
503 Consultations
295 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More