Nonparametric estimation of mark's distribution of an exponential Shot-noise process

Abstract : In this paper, we consider a nonlinear inverse problem occurring in nuclear science. Gamma rays randomly hit a semiconductor detector which produces an impulse response of electric current. Because the sampling period of the measured current is larger than the mean inter arrival time of photons, the impulse responses associated to different gamma rays can overlap: this phenomenon is known as pileup. In this work, it is assumed that the impulse response is an exponentially decaying function. We propose a novel method to infer the distribution of gamma photon energies from the indirect measurements obtained from the detector. This technique is based on a formula linking the characteristic function of the photon density to a function involving the characteristic function and its derivative of the observations. We establish that our estimator converges to the mark density in uniform norm at a logarithmic rate. A limited Monte-Carlo experiment is provided to support our findings.
Type de document :
Article dans une revue
Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2015
Liste complète des métadonnées

Littérature citée [24 références]  Voir  Masquer  Télécharger

https://hal-imt.archives-ouvertes.fr/hal-01164121
Contributeur : Paul Ilhe <>
Soumis le : mardi 26 janvier 2016 - 11:58:32
Dernière modification le : jeudi 11 janvier 2018 - 06:23:39

Fichiers

main2HAL.pdf
Fichiers produits par l'(les) auteur(s)

Licence


Copyright (Tous droits réservés)

Identifiants

  • HAL Id : hal-01164121, version 2
  • ARXIV : 1506.08047

Citation

Paul Ilhe, Eric Moulines, François Roueff, Antoine Souloumiac. Nonparametric estimation of mark's distribution of an exponential Shot-noise process. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2015. 〈hal-01164121v2〉

Partager

Métriques

Consultations de la notice

250

Téléchargements de fichiers

74