The empirical process on Gaussian spherical harmonics
Open Access
- 1 June 2004
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 32 (3) , 1261-1288
- https://doi.org/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.Keywords
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This publication has 14 references indexed in Scilit:
- Probing cosmic microwave background non-Gaussianity using local curvatureMonthly Notices of the Royal Astronomical Society, 2003
- Extended empirical process test for non-Gaussianity in the CMB, with an application to non-Gaussian inflationary modelsPhysical Review D, 2003
- Testing for non-Gaussianity of the cosmic microwave background in harmonic space: An empirical process approachPhysical Review D, 2002
- A Nonparametric Analysis of the Cosmic Microwave Background Power SpectrumThe Astrophysical Journal, 2002
- Statistical Power, the Bispectrum, and the Search for Non‐Gaussianity in the Cosmic Microwave Background AnisotropyThe Astrophysical Journal, 2001
- Acoustic signatures in the primary microwave background bispectrumPhysical Review D, 2001
- Limit Theorems for Random Fields with Singular SpectrumPublished by Springer Nature ,1999
- Weak ConvergencePublished by Springer Nature ,1996
- Convergence of Quantile and Spacings Processes with ApplicationsThe Annals of Mathematical Statistics, 1972
- Convergence Criteria for Multiparameter Stochastic Processes and Some ApplicationsThe Annals of Mathematical Statistics, 1971