Support vector machines (SVMs) are special kernel based methods and belong to
the most successful learning methods since more than a decade. SVMs can
informally be described as a kind of regularized M-estimators for functions and
have demonstrated their usefulness in many complicated real-life problems.
During the last years a great part of the statistical research on SVMs has
concentrated on the question how to design SVMs such that they are universally
consistent and statistically robust for nonparametric classification or
nonparametric regression purposes. In many applications, some qualitative prior
knowledge of the distribution P or of the unknown function f to be estimated is
present or the prediction function with a good interpretability is desired,
such that a semiparametric model or an additive model is of interest.

In this paper we mainly address the question how to design SVMs by choosing
the reproducing kernel Hilbert space (RKHS) or its corresponding kernel to
obtain consistent and statistically robust estimators in additive models. We
give an explicit construction of kernels - and thus of their RKHSs - which
leads in combination with a Lipschitz continuous loss function to consistent
and statistically robust SMVs for additive models. Examples are quantile
regression based on the pinball loss function, regression based on the
epsilon-insensitive loss function, and classification based on the hinge loss
function.