ASYMPTOTICS FOR SPHERICAL 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; Universite Paris Cite; Universite Paris Nanterre; Universite Paris Cite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS601
• 发表日期: 2009
• 页码: 1150-1171
• 关键词: gaussianity; Wavelets; spheres

摘要

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT converaence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.