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Poisson inverse problems

Antoniadis, Anestis and Bigot, Jérémie Poisson inverse problems. (2006) The Annals of Statistics, 34 (5). 2132-2158. ISSN 0090-5364

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Official URL: http://dx.doi.org/10.1214/009053606000000687

Abstract

In this paper we focus on nonparametric estimators in inverse problems for Poisson processes involving the use of wavelet decompositions. Adopting an adaptive wavelet Galerkin discretization, we find that our method combines the well-known theoretical advantages of wavelet–vaguelette decompositions for inverse problems in terms of optimally adapting to the unknown smoothness of the solution, together with the remarkably simple closed-form expressions of Galerkin inversion methods. Adapting the results of Barron and Sheu [Ann. Statist. 19 (1991) 1347–1369] to the context of log-intensity functions approximated by wavelet series with the use of the Kullback–Leibler distance between two point processes, we also present an asymptotic analysis of convergence rates that justifies our approach. In order to shed some light on the theoretical results obtained and to examine the accuracy of our estimates in finite samples, we illustrate our method by the analysis of some simulated examples.

Item Type:Article
Additional Information:Thanks to Institute of Mathematical Statistics editor. The definitive version is available at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1169571792
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > Université Joseph Fourier Grenoble 1 - UJF (FRANCE)
Laboratory name:
Statistics:download
Deposited By: Jérémie Bigot
Deposited On:14 May 2013 09:56

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