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

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 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.
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Submitted on : Friday, April 13, 2018 - 8:46:22 AM
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  • HAL Id : hal-01499914, version 3
  • ARXIV : 1703.10192

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Romain Azaïs, Alexandre Genadot. Estimation of the average number of continuous crossings for non-stationary non-diffusion processes. Journal of Statistical Planning and Inference, Elsevier, In press. ⟨hal-01499914v3⟩

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