High-resolution asymptotics for the angular bispectrum of spherical random fields

Abstract

In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the sample size grows. The results we present are then exploited in a set of procedures aimed at testing non-Gaussianity; for these statistics, we are able to show convergence to functionals of standard Brownian motion under the null hypothesis. Analytic results are also presented on the behavior of the tests in the presence of a broad class of non-Gaussian alternatives. The issue of testing for non-Gaussianity on spherical random fields has recently gained enormous empirical importance, especially in connection with the statistical analysis of cosmic microwave background radiation.

Published at http://dx.doi.org/10.1214/009053605000000903 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Statistical challenges in the analysis of Cosmic Microwave Background radiation
• Ergodicity and Gaussianity for Spherical Random Fields
• Coordinate changed random fields on manifolds
• A Quantitative Central Limit Theorem for the Excursion Area of Random Spherical Harmonics over Subdomains of ${\mathbb{S}}^2$
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• Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
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• Aliasing effects for random fields over spheres of arbitrary dimension
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• Some statistical issues regarding the estimation of $\fnl$ in CMB non-Gaussianity
• Adaptive Nonparametric Regression on Spin Fiber Bundles