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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2020

Hermite density deconvolution

Ousmane B Sacko
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Résumé

We consider the additive model: Z = X + ε, where X and ε are independent. We construct a new estimator of the density of X from n observations of Z. We propose a projection method which exploits the specific properties of the Hermite basis. We study the quality of the resulting estimator by proving a bound on the integrated quadratic risk. We then propose an adaptive estimation procedure, that is a method of selecting a relevant model. We check that our estimator reaches the classical convergence speeds of deconvolution. Numerical simulations are proposed and a comparison with the results of the method proposed in Comte and Lacour (2011) is performed.
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Dates et versions

hal-01978591 , version 1 (11-01-2019)

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Ousmane B Sacko. Hermite density deconvolution. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2020, 17, pp.419-443. ⟨10.30757/ALEA.v17-17⟩. ⟨hal-01978591⟩
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