The empirical process on Gaussian spherical harmonics

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.

References in corpus (6)

• Acoustic Signatures in the Primary Microwave Background Bispectrum
• Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy
• Probing CMB Non-Gaussianity Using Local Curvature
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Cited by in corpus (3)

• High-resolution asymptotics for the angular bispectrum of spherical random fields
• Search for non-Gaussianity in pixel, harmonic and wavelet space: compared and combined
• Ergodicity and Gaussianity for Spherical Random Fields