Linear wavelet estimation in regression with additive and multiplicative noise

Abstract : 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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Submitted on : Thursday, February 14, 2019 - 7:14:49 PM
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  • HAL Id : hal-01877543, version 2

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Christophe Chesneau, Junke Kou, Fabien Navarro. Linear wavelet estimation in regression with additive and multiplicative noise. 2019. ⟨hal-01877543v2⟩

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