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arXiv · 1311.0834

Smooth backfitting in additive inverse regression

Nicolai Bissantz·Holger Dette·Thimo Hildebrandt
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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.

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Nicolai Bissantz, Holger Dette, Thimo Hildebrandt. 2013-11-04. Smooth backfitting in additive inverse regression. https://arxiv.org/abs/1311.0834

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