Robust backfitting estimators for additive models

BOENTE, GRACIELA; MARTÍNEZ, ALEJANDRA; SALIBIAN-BARRERA, MATÍAS

Halle

Conferencia; International Conference on Robust Statistics (ICORS 2014); 2014

the University of Halle, the University of Cassino and the University of Naples

As is well known, kernel estimators of the regression function in nonparametric multivariate regression models suffer from the so-called curse of dimensionality, which occurs because the number of observations lying in neighbourhoods of fixed radii decreases exponentially with the dimension. Additive models are widely used to avoid the difficulty of estimating regression functions of several covariates without using a parametric model. They generalize linear models, are easily interpretable, and are not affected by the curse of the dimensionality. Different estimation procedures for these methods have been proposed in the literature. It is easy to see that most of these estimators can be unduly affected by a small proportion of atypical observations, since they are based on local averages or local polynomials. In particular, the effect of a response outlier will be large if the related covariates are close to the point in which the regression function needs to be estimated. For that reason, robust procedures to estimate the components of an additive model are needed. To solve this problem, we consider a robust back?fitting algorithm based on local kernel polynomials. These estimators simultaneously avoid the curse of dimensionality and the sensitivity to atypical observations. Fisher consistency is derived under mild conditions and a simulation simulation is performed to compare our proposal with the usual backfitting algorithm.