The Annals of Statistics

Asymptotics for spherical needlets

P. Baldi, G. Kerkyacharian, D. Marinucci, and D. Picard

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 3 (2009), 1150-1171.

Dates
First available in Project Euclid: 10 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1239369018

Digital Object Identifier
doi:10.1214/08-AOS601

Mathematical Reviews number (MathSciNet)
MR2509070

Zentralblatt MATH identifier
1160.62087

Subjects
Primary: 62M40: Random fields; image analysis 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles
Secondary: 62G20: Asymptotic properties

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

Citation

Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D. Asymptotics for spherical needlets. Ann. Statist. 37 (2009), no. 3, 1150--1171. doi:10.1214/08-AOS601. https://projecteuclid.org/euclid.aos/1239369018


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