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 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.
"Adaptive density estimation for directional data using needlets." Ann. Statist. 37 (6A) 3362 - 3395, December 2009. https://doi.org/10.1214/09-AOS682