  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. We focus in this paper on
stritcly increasing and continuous transformations. 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.
