Marginal integration $M-$estimators for additive models

TL;DR

This paper introduces a robust marginal integration estimator for additive models that combines local polynomials, offering improved robustness and efficiency over classical methods, especially in the presence of outliers.

Contribution

It proposes a new robust estimator for additive model components that integrates local polynomial fitting with marginal integration, enhancing robustness and asymptotic properties.

Findings

Estimator is consistent and asymptotically normal.

Simulation shows improved robustness over classical methods.

Estimator maintains efficiency with outliers present.

Abstract

Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal univariate rate. Beyond backfitting, marginal integration is a common procedure to estimate each component. In this paper, we propose a robust estimator of the additive components which combines local polynomials on the component to be estimated and marginal integration. 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.