Adaptive density estimation for directional data using needlets

TL;DR

This paper introduces a new adaptive density estimation method for spherical directional data using needlets, a type of wavelet, with proven optimality and applications in astrophysics.

Contribution

It presents a novel thresholding procedure with needlets for density estimation on the sphere, establishing its minimax optimality.

Findings

Proposed method achieves minimax optimality.

Applicable to astrophysical data analysis.

Demonstrates effectiveness on directional data.

Abstract

This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its optimality. We are motivated by astrophysical applications, in particular in connection with the analysis of ultra high energy cosmic rays.