Robust estimators in additive models with missing responses

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

Cadiz

Conferencia; II ISNPS (International Society of Non Parametric Statistics) Conference; 2014

International Society of Non Parametric Statistics

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 models have been proposed in the literature, and some of them have also been extended to the situation when the data may contain missing responses. 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. For that reason, robust procedures to estimate the components of an additive model are needed. We consider robust estimators for additive models based on local polynomials that can also be used on data sets with missing responses. These estimators simultaneously avoid the curse of dimensionality and the sensitivity to atypical observations. Our proposal is based on the method of marginal integration, and adapted to the missing responses situation. If time permits, we will also introduce a robust kernel estimator for additive models via the back-fitting algorithm.