Electronic Journal of Statistics

Nonparametric estimation of mark’s distribution of an exponential shot-noise process

Paul Ilhe, Éric Moulines, Francois Roueff, and Antoine Souloumiac

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Abstract

In this paper, we consider a nonlinear inverse problem occuring 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 interarrival 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 polynomial rate. A limited Monte-Carlo experiment is provided to support our findings.

Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 3098-3123.

Dates
Received: June 2015
First available in Project Euclid: 20 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1453298266

Digital Object Identifier
doi:10.1214/15-EJS1103

Mathematical Reviews number (MathSciNet)
MR3450757

Zentralblatt MATH identifier
1334.62050

Subjects
Primary: 45Q05: Inverse problems 60G10: Stationary processes 62G07: Density estimation 62M05: Markov processes: estimation

Keywords
Shot-noise Lévy-driven Ornstein-Uhlenbeck process nonparametric estimation Markov process empirical processes $\beta$-mixing

Citation

Ilhe, Paul; Moulines, Éric; Roueff, Francois; Souloumiac, Antoine. Nonparametric estimation of mark’s distribution of an exponential shot-noise process. Electron. J. Statist. 9 (2015), no. 2, 3098--3123. doi:10.1214/15-EJS1103. https://projecteuclid.org/euclid.ejs/1453298266


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