# Nonparametric estimation in a regression model with additive and multiplicative noise

## TL;DR

This paper introduces two wavelet estimators for nonparametric regression models with both additive and multiplicative noise, achieving fast convergence rates under weak conditions, supported by numerical experiments.

## Contribution

The paper proposes novel wavelet estimators for complex noise models in nonparametric regression, with theoretical convergence guarantees and practical validation.

## Key findings

- Estimators achieve fast convergence rates under weak conditions.
- Numerical results support theoretical claims.
- Applicable to models similar to stochastic frontier estimation.

## 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.