Nonparametric regression on closed Riemannian manifolds

Abstract

International audienceThe nonparametric estimation of the regression function of a real-valued random variable Y on a random object X val- ued in a closed Riemannian manifold M is considered. A regression estimator which generalizes kernel regression es- timators on Euclidean sample spaces is introduced. Under classical assumptions on the kernel and the bandwidth se- quence, the asymptotic bias and variance are obtained, and the estimator is shown to converge at the same L2-rate as kernel regression estimators on Euclidean spaces