kNN robustification equivariant nonparametric regression estimators for functional ergodic data

Abstract

We discuss in this paper the robust equivariant nonparametric regression estimators for ergodic data with the k Nearst Neighbour (kNN) method. We consider a new robust regression estimator when the scale parameter is unknown. The principal aim is to prove the almost complete convergence (with rate) for the proposed estimator. Furthermore, a comparison study based on simulated data is also provided to illustrate the finite sample performances and the usefulness of the kNN approach and to prove the highly sensitive of the kNN approach to the presence of even a small proportion of outliers in the data.