Non-parametric regression on the hyper-sphere with uniform design
Résumé
This paper deals with the estimation of a function $f$ defined on the sphere $\Sp^d$ of $\R^{d+1}$ from a sample of noisy observation points. We introduce an estimation procedure based on wavelet-like functions on the sphere called needlets and study two estimators $f^\circledast$ and $f^\bigstar$ respectively made adaptive through the use of a stochastic and deterministic needlet-shrinkage method. We show hereafter that these estimators are nearly-optimal in the minimax framework, explain why $f^\circledast$ outperforms $f^\bigstar$ and run finite sample simulations with $f^\circledast$ to demonstrate that our estimation procedure is easy to implement and fares well in practice. We are motivated by applications in geophysical and atmospheric sciences.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...