M robustified additive nonparametric regression

Additive modelling has been widely used in nonparametric regression to circumvent the curse of dimensionality, by reducing the problem of estimating a multivariate regression function to the estimation of its univariate components. Estimation of these univariate functions, however, can suffer inaccuracy if the data set is contaminated with extreme observations. As detection and removal of outliers in high dimension is much more difficult than in one dimension, we propose an M type marginal integration estimator that automatically corrects the extreme influence of outliers. We establish the robustness and obtain the asymptotic distribution of the M estimator through the functional approach. As a consequence, our results are valid for ,ß-mixing samples under mild constraints. Monte Carlo study confirm our theoretical results.