Abstract
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we analyze its moments and cumulants of arbitrary order and we use these results to establish a multivariate central limit theorem and higher order approximations. The results rely upon combinatorial methods from graph theory and a detailed investigation for the asymptotic behavior of coefficients arising in matrix representation theory for the group of rotations SO(3).
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I am very grateful to an associate editor and two referees for many useful comments, and to M. W. Baldoni and P. Baldi for discussions on an earlier version.
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Marinucci, D. A central limit theorem and higher order results for the angular bispectrum. Probab. Theory Relat. Fields 141, 389–409 (2008). https://doi.org/10.1007/s00440-007-0088-8
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DOI: https://doi.org/10.1007/s00440-007-0088-8
Keywords
- Spherical random fields
- Angular bispectrum
- Central limit theorem
- Higher order approximations
Mathematics Subject Classification (2000)
- Primary: 60G60
- Secondary: 60F05
- 62M15
- 62M40