The empirical process on Gaussian spherical harmonics

2004/05/27 by Domenico Marinucci, Mauro Piccioni
Economics, Econometrics and Finance · Mathematics · #Geometry and complex manifolds #Point processes and geometric inequalities #Stochastic processes and financial applications #math.ST #msc:60F17 #msc:62G20 #msc:62G30 #stat.TH

paper · pdf · doi:10.1214/009053604000000355

published as Annals of Statistics 2004, Vol. 32, No. 3, 1261-1288

openalex publication_date 2004/05/27 · arxiv created 2004/06/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Inter-Scale Correlations as Measures of CMB Gaussianity
• Statistical Power, the Bispectrum, and the Search for Non‐Gaussianity in the Cosmic Microwave Background Anisotropy
• Quantum Theory of Angular Momentum