2015/09/14 by Graciela Boente, Boente, Graciela, Alejandra Martínez‐Monés +2 · 1 citation
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Statistical Methods and Inference #stat.ME
paper · pdf · doi:10.48550/arxiv.1509.04334
arxiv created 2015/09/14 · arxiv updated 2015/09/16
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.