Block Thresholding on the Sphere

Abstract

The aim of this paper is to study nonparametric regression estimators on the sphere based on needlet block thresholding. The block thresholding procedure proposed here follows the method introduced by Hall et al. (Ann. Stat. 26, 922–942, 1998, Stat. Sin. 9, 33–49, 1999), which we modify to exploit the properties of spherical needlets. We establish convergence rates, and we show that they attain adaptivity over Besov balls in the regular region. This work is strongly motivated by issues arising in Cosmology and Astrophysics, concerning in particular the analysis of Cosmic rays.