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Uniform Deconvolution for Poisson Point Processes

Bonnet, Anna; Lacour, Claire; Picard, Franck; Rivoirard, Vincent (2020), Uniform Deconvolution for Poisson Point Processes. https://basepub.dauphine.psl.eu/handle/123456789/22282

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02964117
Date
2020
Series title
Cahier de recherche du CEREMADE
Pages
32
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Author(s)
Bonnet, Anna
Laboratoire de Probabilités, Statistiques et Modélisations [LPSM (UMR_8001)]
Lacour, Claire
Laboratoire Analyse et Mathématiques Appliquées [LAMA]
Picard, Franck
Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 [LBBE]
Rivoirard, Vincent
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle and minimax points of view, and provide new lower bounds when the intensity belongs to a Sobolev ball. By developing the Goldenshluger-Lepski methodology in the case of deconvolution for Pois-son processes, we propose an optimal data-driven selection of the kernel's bandwidth, and we provide a heuristic framework to calibrate the estimator in practice. Our method is illustrated on the spatial repartition of replication origins along the human genome.
Subjects / Keywords
Convolution; Poisson process; Adaptive estimation