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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2017

Minimax regression estimation for Poisson coprocess

Résumé

For a Poisson point process X, Itô's famous chaos expansion implies that every square integrable regression function r with covariate X can be decomposed as a sum of multiple stochastic integrals called chaos. In this paper, we consider the case where r can be decomposed as a sum of δ chaos. In the spirit of Cadre and Truquet (2015), we introduce a semiparametric estimate of r based on i.i.d. copies of the data. We investigate the asymptotic minimax properties of our estimator when δ is known. We also propose an adaptive procedure when δ is unknown.
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Dates et versions

hal-01430576 , version 1 (10-01-2017)

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Benoît Cadre, Nicolas Klutchnikoff, Gaspar Massiot. Minimax regression estimation for Poisson coprocess. ESAIM: Probability and Statistics, 2017, 21, pp.138-158. ⟨10.1051/ps/2017004⟩. ⟨hal-01430576⟩
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