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June 2004 The empirical process on Gaussian spherical harmonics
Domenico Marinucci, Mauro Piccioni
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Ann. Statist. 32(3): 1261-1288 (June 2004). DOI: 10.1214/009053604000000355

Abstract

We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background radiation.

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Domenico Marinucci. Mauro Piccioni. "The empirical process on Gaussian spherical harmonics." Ann. Statist. 32 (3) 1261 - 1288, June 2004. https://doi.org/10.1214/009053604000000355

Information

Published: June 2004
First available in Project Euclid: 24 May 2004

zbMATH: 1051.60035
MathSciNet: MR2065205
Digital Object Identifier: 10.1214/009053604000000355

Subjects:
Primary: 60F17 , 62G20 , 62G30

Keywords: Cosmic Microwave Background radiation , Empirical processes , Gaussian spherical harmonics , weak convergence

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 3 • June 2004
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