Statistical estimation of a shot-noise process

Overview & Synopsis

In the context of gamma-spectroscopy, this thesis introduces new nonparametric estimators of the intensity and the mark’s density of a shot-noise process based on a finite sample of low-frequency observations of this stochastic process. The methods developed exploit a nonlinear functional equation linking the characteristic function of the marginal law of the shot-noise with the mark’s density function. They are particularly time-efficient and perform well even for processes with high intensity. The performances of the methods are quantitatively studied and illustrations are provided both on simulated datasets and real datasets stemming from the CEA. In particular, our methods corrects the multiple peak artefacts that arises with classical techniques.