Robust equivariant nonparametric regression estimators for strongly mixing data using a k nearest neighbour approach

Abstract

We discuss in this paper the robust equivariant nonparametric regression estimators for strong mixing data with the k Nearest 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.