Robust nonparametric regression on Riemannian manifolds

Guillermo Henry and Daniela Rodriguez

Journal of Nonparametric Statistics, 2009, vol. 21, issue 5, 611-628

Abstract: 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.

Date: 2009
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DOI: 10.1080/10485250902846439

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