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 quasiexponentially 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.

Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D. (2009). Asymptotics for spherical needlets. ANNALS OF STATISTICS, 37(3), 1150-1171 [10.1214/08-AOS601].

Asymptotics for spherical needlets

BALDI, PAOLO;MARINUCCI, DOMENICO;
2009-01-01

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 quasiexponentially 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.
2009
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Con Impact Factor ISI
Central limit theorem; High-frequency asymptotics; Random fields; Spherical needlets; Tests for Gaussianity and isotropy
Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D. (2009). Asymptotics for spherical needlets. ANNALS OF STATISTICS, 37(3), 1150-1171 [10.1214/08-AOS601].
Baldi, P; Kerkyacharian, G; Marinucci, D; Picard, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23717
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