Smooth backfitting in additive inverse regression

Abstract

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.

Keywords: inverse regression; additive models; curse of dimensionality; smooth backfitting Mathematical subject classification: Primary: 62G20; Secondary 15A29 Pages: 26 Figures: 3