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

Estimation of the Transformation Function in Fully Nonparametric Transformation Models with Heteroscedasticity