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

• 成果类型: Article
• 署名作者: Marinucci, Domenico
• 署名单位: University of Rome Tor Vergata
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000903
• 发表日期: 2006
• 页码: 1-41
• 关键词: probe wmap observations; Non-Gaussianity; excursion sets; microwave; asymmetries; MAPS

摘要

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.