Marginal integration M-estimators for additive models

BOENTE, GRACIELA; MARTÍNEZ, ALEJANDRA

TEST

SPRINGER

Lugar: Berlin; Año: 2017 vol. 26 p. 231 - 260

1133-0686

Additive regression models have a long history in multivariate nonparametricregression. They provide a model in which the regression function isdecomposed 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 backfitting, marginal integration 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 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 efficiency properties.