  Completely nonparametric transformation models with heteroscedastic errors
are considered. Despite their flexibility, such models have rarely been used so
far, since estimators of the model components have been missing and even
identification of such models has not been clear until very recently. The
results of Kloodt (2020) are used to construct the first two estimators of the
transformation function in these models. While the first estimator converges to
the true transformation function at a parametric rate, the second estimator can
be obtained by an explicit formula and is less computationally demanding.
Finally, a simulation study is followed by some concluding remarks. Assumptions
and proofs can be found in the appendix.
