estimator were generalized for nonparametric regression models by Colling and Van Keilegom (2016). All literature cited above is about mean or quantile regression. In contrast in the paper at hand we consider boundary regression models. Such nonparametric regression models with one-sided errors have been considered, among others, by Hall and Van Keilegom (2009), Meister and Rei[ß]{} (2013), Jirak, Meister and Rei[ß]{} (2014) and Drees, Neumeyer and Selk (2018). Relatedly, estimation of support boundaries have been considered, for instance, by Härdle, Park and Tsybakov (1995), Hall, Park and Stern (1998), Girard and Jacob (2008) and Daouia, Noh and Park (2016). Such models naturally appear when analyzing auctions or records or production frontiers. Unlike conditional mean models, regression models with one-sided errors (as well as quantile regression models) have the attractive feature of equivariance under monotone transformations. Thus in such a model with monotone transformation of the response one can recover the original functional dependence in an easy manner. Similar to Linton et al. (2008) the aim of our transformation is to induce a model where the error distribution does not depend on the covariates. Independence of errors and covariates is a very typical assumption in regression models. For boundary models this 