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arXiv · 1405.6584

The additive model with different smoothness for the components

Sara van de Geer·Alan Muro
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Abstract

We consider an additive regression model consisting of two components $f^0$ and $g^0$, where the first component $f^0$ is in some sense "smoother" than the second $g^0$. Smoothness is here described in terms of a semi-norm on the class of regression functions. We use a penalized least squares estimator $(\hat f, \hat g)$ of $(f^0, g^0)$ and show that the rate of convergence for $\hat f $ is faster than the rate of convergence for $\hat g$. In fact, both rates are generally as fast as in the case where one of the two components is known. The theory is illustrated by a simulation study. Our proofs rely on recent results from empirical process theory.

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Sara van de Geer, Alan Muro. 2014-05-26. The additive model with different smoothness for the components. https://arxiv.org/abs/1405.6584

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