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Nonparametric estimation in a regression model with additive and multiplicative noise

Authors
  • Chesneau, Christophe
  • Kolei, Salima El
  • Kou, Junke
  • Navarro, Fabien
Type
Preprint
Publication Date
Jun 20, 2020
Submission Date
Jun 18, 2019
Identifiers
DOI: 10.1016/j.cam.2020.112971
Source
arXiv
License
Yellow
External links

Abstract

In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context. We prove that they achieve fast convergence rates under the mean integrated square error over Besov spaces. The obtained rates have the particularity of being established under weak conditions on the model. A numerical study in a context comparable to stochastic frontier estimation (with the difference that the boundary is not necessarily a production function) supports the theory.

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