equidistant design framework and examine the two regression functions $h_0(x)= 10(x-\textstyle{\frac 12})^2$ and $h_0(x)= \textstyle{\frac 12}\sin(2\pi x)+4x$ for two different error distributions, namely the Weibull distribution with scale parameter $1$ and shape parameter $3$ and the exponential distribution with mean $1/3$. We consider samples of size $n=50$ and $n=100$. It means that we investigate the following four models $$\begin{aligned}
h_0(x)= 10(x-\textstyle{\frac 12})^2   && \text{with} \ \ \ \varepsilon\sim \mbox{Weibull}(1,3)  \label{simu1}\\
h_0(x)= 10(x-\textstyle{\frac 12})^2  && \text{with} \ \ \ \varepsilon\sim \mbox{Exp}(3)\label{simu2}\\
h_0(x)= \textstyle{\frac 12}\sin(2\pi x)+4x && \text{with} \ \ \ \varepsilon\sim \mbox{Weibull}(1,3)  \label{simu3}\\
h_0(x)=  \textstyle{\frac 12}\sin(2\pi x)+4x && \text{with} \ \ \ \varepsilon\sim \mbox{Exp}(3). \label{simu4}\end{aligned}$$ Figures \[graphic1\] and \[graphic2\] show realizations of models (\[simu1\]) and (\[simu3\]). The bandwidth $b_n=n^{-1/3}$ is chosen accordingly to Drees et al. (2018) and simulations are based on $1000$ iterations. We use the Epanechnikov kernel to smooth the boundary curve estimator and compare the results for two smoothing parameters $a_n=b_n/2$ and $a_n=b_n/20$. The transformation parameter estimator is as in (\[deftheta\]) on the interval $[-0.5,2.5]$, where the semi-norm in the criterion function $M_n(\vartheta)$ is chosen as in $(i)$, $(ii)$, $(iii),$ and $(iv)$ in the examples of Condition \[N1\]. In the following we denote the according estimators as TKS, 