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Hermite density deconvolution

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01978591
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Submitted on : Friday, January 11, 2019 - 3:57:53 PM
Last modification on : Friday, April 10, 2020 - 5:20:43 PM

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  • HAL Id : hal-01978591, version 1

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Ousmane B Sacko. Hermite density deconvolution. 2019. ⟨hal-01978591⟩

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