Resumen de Nonparametric regression on the hyper-sphere with uniform design

Jean-Baptiste Monnier

• This paper deals with the estimation of a function f defined on the sphere Sd of ℝd+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 ⊛ and f★ 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 ⊛ outperforms f★ , and run finite-sample simulations with f ⊛ 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.