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Adaptive nonparametric estimation of a component density in a two-class mixture model

Abstract : A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly weighted kernel estimator with a fully data-driven bandwidth selection method, in the spirit of the Goldenshluger and Lepski method. An oracle-type inequality for the pointwise quadratic risk is derived as well as convergence rates over Hölder smoothness classes. The theoretical results are illustrated by numerical simulations.
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https://hal.archives-ouvertes.fr/hal-02909601
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Submitted on : Thursday, July 30, 2020 - 4:58:34 PM
Last modification on : Wednesday, September 23, 2020 - 4:31:25 AM

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  • HAL Id : hal-02909601, version 1

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Gaëlle Chagny, Antoine Channarond, van Ha Hoang, Angelina Roche. Adaptive nonparametric estimation of a component density in a two-class mixture model. 2020. ⟨hal-02909601⟩

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