Boundary regression models naturally arise in many applications for instance when analysing auctions or records but also in production frontiers and image
analysis. Before fitting a regression model it is very common to transform the response variable to gain effciency in the statistical inference. In this talk, we will consider parametric transformations that induce independence of the error distribution from the points of measurements. In such a context, if the transformation of the response is monotone, the attractive feature is that one may recover the original functional dependence in an easy manner. The main purpose of this talk is to investigate the consistency of an estimator based on a minimum distance approach in the context of nonparametric regression models with one-sided errors. In particular, we estimate the transformation parameter
and give mild model assumptions under which the estimator is consistent, for both random covariates and fixed design points. The small sample behavior will be shown in a simulation study using the so-called Yeo-Johnson transformations.