  Asymptotic equivalence in Le Cam's sense for nonparametric regression
experiments is extended to the case of non-regular error densities, which have
jump discontinuities at their endpoints. We prove asymptotic equivalence of
such regression models and the observation of two independent Poisson point
processes which contain the target curve as the support boundary of its
intensity function. The intensity of the point processes is of order of the
sample size $n$ and involves the jump sizes as well as the design density. The
statistical model significantly differs from regression problems with Gaussian
or regular errors, which are known to be asymptotically equivalent to Gaussian
white noise models.
