Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7547046 | Journal of Statistical Planning and Inference | 2019 | 20 Pages |
Abstract
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 dâ¥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 a 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Romain Azaïs, Alexandre Genadot,