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Linear wavelet estimation in regression with additive and multiplicative noise

Résumé

In this paper, we deal with the estimation of an unknown function from a nonparametric regression model with both additive and multiplicative noises. The case of the uniform multiplicative noise is considered. We develop a projection es-timator based on wavelets for this problem. We prove that it attains a fast rate of convergence under the mean integrated square error over Besov spaces. A practical extension to automatically select the truncation parameter of this estimator is discussed. A numerical study illustrates the usefulness of this extension.
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Dates et versions

hal-01877543 , version 1 (19-09-2018)
hal-01877543 , version 2 (14-02-2019)

Identifiants

Citer

Christophe Chesneau, Junke Kou, Fabien Navarro. Linear wavelet estimation in regression with additive and multiplicative noise. Conference of the International Society for Non-Parametric Statistics, Jun 2018, Salerno, Italy. ⟨10.1007/978-3-030-57306-5_13⟩. ⟨hal-01877543v2⟩
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