  In a recent paper Birke and Bissantz (2008) considered the problem of
nonparametric estimation in inverse regression models with convolution-type
operators. For multivariate predictors nonparametric methods suffer from the
curse of dimensionality and we consider inverse regression models with the
additional qualitative assumption of additivity. In these models several
additive estimators are studied. In particular, we investigate estimators under
the random design assumption which are applicable when observations are not
available on a grid. Finally, we compare this estimator with the marginal
integration and the non-additive estimator by means of a simulation study. It
is demonstrated that the new method yields a substantial improvement of the
currently available procedures.
