Additive regression models have a long history in multivariate non-
parametric regression. They provide a model in which the regression function is
decomposed as a sum of functions, each of them depending only on a single explana-
tory variable. The advantage of additive models over general non-parametric regression
models is that they allow to obtain estimators converging at the optimal univariate rate
avoiding the so-called curse of dimensionality. Beyond backfitting, marginal integra-
tion is a common procedure to estimate each component in additive models. In this
paper, we propose a robust estimator of the additive components which combines local
polynomials on the component to be estimated with the marginal integration proce-
dure. The proposed estimators are consistent and asymptotically normally distributed.
A simulation study allows to show the advantage of the proposal over the classical one
when outliers are present in the responses, leading to estimators with good robustness
and efficiency properties.

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• Marginal integration M-estimators for additive models