ADAPTIVE DENSITY ESTIMATION FOR DIRECTIONAL DATA USING NEEDLETS

• 成果类型: Article
• 署名作者: Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
• 署名单位: University of Rome Tor Vergata; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS682
• 发表日期: 2009
• 页码: 3362-3395
• 关键词: strong uniform-convergence; asymptotic minimax risk; RIEMANNIAN-MANIFOLDS; spherical data; spheres

摘要

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.