A central limit theorem and higher order results for the angular bispectrum

✍ Scribed by Domenico Marinucci

• Book ID: 106137820
• Publisher: Springer
• Year: 2007
• Tongue: English
• Weight: 272 KB
• Volume: 141
• Category: Article
• ISSN: 1432-2064
• DOI: 10.1007/s00440-007-0088-8

✦ Synopsis

The angular bispectrum of spherical random fields has recently gained anenormous importance, especially in connection with statistical inference on cosmologicaldata. In this paper, we analyze its moments and cumulants of arbitrary order andwe use these results to establish a multivariate central limit theorem and higher orderapproximations. The results rely upon combinatorial methods from graph theory anda detailed investigation for the asymptotic behavior of coefficients arising in matrixrepresentation theory for the group of rotations SO(3).