Open Access
June 2009 Asymptotics for spherical needlets
P. Baldi, G. Kerkyacharian, D. Marinucci, D. Picard
Ann. Statist. 37(3): 1150-1171 (June 2009). DOI: 10.1214/08-AOS601


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 convergence 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.


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P. Baldi. G. Kerkyacharian. D. Marinucci. D. Picard. "Asymptotics for spherical needlets." Ann. Statist. 37 (3) 1150 - 1171, June 2009.


Published: June 2009
First available in Project Euclid: 10 April 2009

zbMATH: 1160.62087
MathSciNet: MR2509070
Digital Object Identifier: 10.1214/08-AOS601

Primary: 60F05 , 60F17 , 62M40
Secondary: 62G20

Keywords: central limit theorem , High-frequency asymptotics , Random fields , spherical needlets , tests for Gaussianity and isotropy

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 3 • June 2009
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