Nonparametric regression on closed Riemannian manifolds
Résumé
The 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.
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