Academic Journal
Estimation of the average number of continuous crossings for non-stationary non-diffusion processes
| العنوان: | Estimation of the average number of continuous crossings for non-stationary non-diffusion processes |
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| المؤلفون: | Azaïs, Romain, Genadot, Alexandre |
| المساهمون: | Simulation et Analyse de la morphogenèse in siliCo (MOSAIC), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Reproduction et développement des plantes (RDP), École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Université de Lyon-Institut National de la Recherche Agronomique (INRA)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Quality control and dynamic reliability (CQFD), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | ISSN: 0378-3758. |
| بيانات النشر: | HAL CCSD Elsevier |
| سنة النشر: | 2019 |
| المجموعة: | Université de Rennes 1: Publications scientifiques (HAL) |
| مصطلحات موضوعية: | Average number of crossings, Piecewise deterministic process, Plug-in estimators, [STAT.ME]Statistics [stat]/Methodology [stat.ME], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] |
| الوصف: | International audience ; 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. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/1703.10192; ARXIV: 1703.10192 |
| DOI: | 10.1016/j.jspi.2018.04.002 |
| الاتاحة: | https://hal.science/hal-01499914 https://hal.science/hal-01499914v3/document https://hal.science/hal-01499914v3/file/crossings.pdf https://doi.org/10.1016/j.jspi.2018.04.002 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.3AA57555 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.jspi.2018.04.002 |
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