Adaptive density estimation for directional data using needlets

G. Kerkyacharian (1) , P. Baldi , D. Marinucci , D. Picard (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

G. Kerkyacharian, P. Baldi, D. Marinucci, D. Picard. Adaptive density estimation for directional data using needlets. Annals of Statistics, 2009, 37 (6A), pp.3362-3395. ⟨10.1214/09-AOS682⟩. ⟨hal-00441240⟩