Nonparametric estimation in a regression model with additive and multiplicative noise

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 th...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2020-12, Vol.380, p.112971, Article 112971
Main Authors: Chesneau, Christophe, El Kolei, Salima, Kou, Junke, Navarro, Fabien
Format: Article
Language:English
Subjects:
Mathematics
Methodology
Multiplicative regression models
Nonparametric frontier
Nonparametric regression
Rates of convergence
Statistics
Wavelets
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2020.112971