Block Thresholding on the Sphere

TL;DR

This paper develops and analyzes a nonparametric regression estimator on the sphere using needlet block thresholding, with applications in Cosmology and Astrophysics, demonstrating adaptive convergence rates over Besov spaces.

Contribution

It introduces a needlet-based block thresholding method for spherical nonparametric regression, extending previous techniques to exploit spherical properties and achieve adaptive convergence rates.

Findings

Achieves adaptive convergence rates over Besov spaces.

Demonstrates effectiveness in cosmic ray data analysis.

Extends thresholding techniques to spherical needlets.

Abstract

The aim of this paper is to study the nonparametric regression estimators on the sphere built by the needlet block thresholding. The block thresholding procedure proposed here follows the method introduced by Hall, Kerkyacharian and Picard in [Hall, Kerkyacharian, Picard, (1998), (1999)], modified to exploit the properties of the spherical standard needlets. Therefore, we will investigate on their convergence rates, attaining their adaptive properties over the Besov balls. This work is strongly motivated by issues arising in Cosmology and Astrophysics, concerning in particular the analysis of cosmic rays.