Smooth Backfitting in Additive Inverse Regression

• Activity Number: 220
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Holger Dette* and Nicolai Bissantz and Thimo Hildebrandt
• Companies: Ruhr University Bochum and Ruhr University Bochum and Ruhr University Bochum
• Keywords: inverse regression ; curse of dimensionality ; additive models ; smooth backfitting

Abstract

We consider the problem of estimating an additive regression function in an inverse regression model with a convolution type operator. A smooth backfitting procedure is developed and asymptotic normality of the resulting estimator is established. Compared to other methods 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 integration method at least by a factor two with respect to the integrated mean squared error criterion.