Adaptive density estimation for directional data using needlets

P. Baldi (1, 2) , G. Kerkyacharian (2) , D. Marinucci (1) , D. Picard (2)

1 DIPMAT - Dipartimento di Matematica [Roma II]
2 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 {\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.

Domaines: Statistiques [math.ST]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]

P. Baldi, G. Kerkyacharian, D. Marinucci, D. Picard. Adaptive density estimation for directional data using needlets. 2008. ⟨hal-00319968⟩