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abstract: 'In the context of nonparametric regression models with one-sided errors, we consider parametric transformations of the response variable in order to obtain independence between the errors and the covariates. In view of estimating the tranformation parameter, we use a minimum distance approach and show the uniform consistency of the estimator under mild conditions. The boundary curve, i.e. the regression function, is estimated applying a smoothed version of a local constant approximation for which we also prove the uniform consistency. We deal with both cases of random covariates and deterministic (fixed) design points. To highlight the applicability of the procedures and to demonstrate their performance, the small sample behavior is investigated in a simulation study using the so-called Yeo-Johnson transformations.'
author:
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    [Natalie Neumeyer, Leonie Selk]{} and [Charles Tillier]{}\
    Department of Mathematics, University of Hamburg
title: '**Semi-parametric transformation boundary regression models[^1]**'
---

[**Key words:**]{} Box-Cox transformations, frontier estimation, minimum-distance estimation, local constant approximation, boundary models, nonparametric regression, Yeo-Johnson transformations

Introduction
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Before fitting a regression model it is very common in applications to transform the response variable. The aim of the transformation is to gain efficiency in the statistical inference, for instance, by reducing skewness or inducing a 