The Annals of Statistics

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

Domenico Marinucci

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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.

Article information

Source
Ann. Statist., Volume 34, Number 1 (2006), 1-41.

Dates
First available in Project Euclid: 2 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1146576254

Digital Object Identifier
doi:10.1214/009053605000000903

Mathematical Reviews number (MathSciNet)
MR2275233

Zentralblatt MATH identifier
1104.60020

Subjects
Primary: 60G60: Random fields
Secondary: 60F17: Functional limit theorems; invariance principles 62M15: Spectral analysis 85A40: Cosmology {For relativistic cosmology, see 83F05}

Keywords
Spherical random fields bispectrum Gaussianity cosmic microwave background radiation

Citation

Marinucci, Domenico. High-resolution asymptotics for the angular bispectrum of spherical random fields. Ann. Statist. 34 (2006), no. 1, 1--41. doi:10.1214/009053605000000903. https://projecteuclid.org/euclid.aos/1146576254


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