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Support vector machines (SVMs) are special kernel based methods and belong tothe most successful learning methods since more than a decade. SVMs caninformally be described as a kind of regularized M-estimators for functions andhave demonstrated their usefulness in many complicated real-life problems.During the last years a great part of the statistical research on SVMs hasconcentrated on the question how to design SVMs such that they are universallyconsistent and statistically robust for nonparametric classification ornonparametric regression purposes. In many applications, some qualitative priorknowledge of the distribution P or of the unknown function f to be estimated ispresent 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 choosingthe reproducing kernel Hilbert space (RKHS) or its corresponding kernel toobtain consistent and statistically robust estimators in additive models. Wegive an explicit construction of kernels - and thus of their RKHSs - whichleads in combination with a Lipschitz continuous loss function to consistentand statistically robust SMVs for additive models. Examples are quantileregression based on the pinball loss function, regression based on theepsilon-insensitive loss function, and classification based on the hinge lossfunction.

Support Vector Machines for Additive Models: Consistency and Robustness