  We consider the problem of estimating an additive regression function in an
inverse regres- sion model with a convolution type operator. A smooth
backfitting procedure is developed and asymptotic normality of the resulting
estimator is established. Compared to other meth- ods for the estimation in
additive models the new approach neither requires observations on a regular
grid nor the estimation of the joint density of the predictor. It is also
demonstrated by means of a simulation study that the backfitting estimator
outperforms the marginal in- tegration method at least by a factor two with
respect to the integrated mean squared error criterion.
