Robust nonparametric regression on Riemannian manifolds

GUILLERMO HENRY; DANIELA RODRIGUEZ

JOURNAL OF NONPARAMETRIC STATISTICS

Taylor & Francis

Lugar: London; Año: 2009 vol. 21 p. 611 - 628

1048-5252

In this study, we introduce two families of robust kernel-based regression estimators when the regressors are random objects taking values in a Riemannian manifold. The first proposal is a local M-estimator based on kernel methods, adapted to the geometry of the manifold. For the second proposal, the weights are based on k-nearest neighbour kernel methods. Strong uniform consistent results as well as the asymptotical normality of both families are established. Finally, a Monte Carlo study is carried out to compare the performance of the robust proposed estimators with that of the classical ones, in normal and contaminated samples and a cross-validation method is discussed.