Marginal integration M -estimators for additive models

BOENTE, GRACIELA; MARTINEZ, ALEJANDRA

Marrakech

Congreso; 61st World Statistics Congress; 2017

International Statistical Institute

Additive regression models have a long history in multivariate nonparametric 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 explanatory 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 backtting, marginal integration is a common procedure to estimate each component in additive models. In this work, we propose a robust estimator of the additive components which combines local polynomials on the component to be estimated with the marginal integration procedure. 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 eciency properties.