A1240
Title: Robust bootstrap inference for nonparametric regression
Authors: Stefan Van Aelst - University of Leuven (Belgium) [presenting]
Matias Salibian-Barrera - The University of British Columbia (Canada)
Abstract: Robust penalized spline estimators are considered for nonparametric regression models where the response depends on the predictor through an unknown smooth function f. The errors are assumed to be independent and identically distributed according to a symmetric distribution with center zero. The loss function provides robustness against potential outliers while smoothness is regularized by a penalty term. The estimators can be rewritten in a penalized weighted least squares form, which facilitates the development of an iteratively weighted least squares algorithm for computation. Asymptotic results are insufficiently developed for robust spline-based estimators to construct robust inference based on asymptotic theory. Bootstrap methods are explored to develop robust inference procedures. To obtain desirable results, the bias due to smoothing must be taken into account when bootstrapping nonparametric regression estimators. Bootstrap methods are investigated to develop robust inference based on robust spline-based estimators and their performance is assessed.
