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Uniform Deconvolution for Poisson Point Processes

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02964117
Contributor : Claire Lacour Connect in order to contact the contributor
Submitted on : Friday, July 1, 2022 - 3:02:06 PM
Last modification on : Saturday, September 24, 2022 - 2:36:04 PM

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  • HAL Id : hal-02964117, version 2
  • ARXIV : 2010.04557

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Anna Bonnet, Claire Lacour, Franck Picard, Vincent Rivoirard. Uniform Deconvolution for Poisson Point Processes. Journal of Machine Learning Research, Microtome Publishing, 2022, 23 (194), pp.1--36. ⟨hal-02964117v2⟩

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