Report
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 |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Statistics - Methodology, Mathematics - Probability |
| الوصف: | 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 $d\geq2$). 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: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1703.10192 |
| رقم الانضمام: | edsarx.1703.10192 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |