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

DOI10.1214/009053605000000903zbMath1104.60020arXivmath/0502434OpenAlexW2047037194MaRDI QIDQ2493544

Domenico Marinucci

Publication date: 21 June 2006

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502434

zbMATH Keywords

spherical harmonicsGaussianityspectral representationcosmic microwave background radiation

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Stationary stochastic processes (60G10) Inference from stochastic processes and spectral analysis (62M15) Functional limit theorems; invariance principles (60F17) Astrophysical cosmology (85A40)

Related Items (28)

Adaptive global thresholding on the sphere ⋮ Subsampling needlet coefficients on the sphere ⋮ Mixed needlets ⋮ Angular spectra for non-Gaussian isotropic fields ⋮ Time dependent random fields on spherical non-homogeneous surfaces ⋮ Spin wavelets on the sphere ⋮ Group representations and high-resolution central limit theorems for subordinated spherical random fields ⋮ The needlets bispectrum ⋮ Spin needlets spectral estimation ⋮ Adaptive nonparametric regression on spin fiber bundles ⋮ A central limit theorem and higher order results for the angular bispectrum ⋮ A quantitative central limit theorem for the excursion area of random spherical harmonics over subdomains of S2 ⋮ Multivariate lag-windows and group representations ⋮ High-frequency asymptotics for subordinated stationary fields on an abelian compact group ⋮ High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus ⋮ Coordinates changed random fields on the sphere ⋮ Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem ⋮ Fractional Cauchy problems on compact manifolds ⋮ Statistical challenges in the analysis of cosmic microwave background radiation ⋮ Asymptotics for spherical needlets ⋮ Representations of SO(3) and angular polyspectra ⋮ Aliasing effects for random fields over spheres of arbitrary dimension ⋮ The defect of random hyperspherical harmonics ⋮ On Spectral Representations of Tensor Random Fields on the Sphere ⋮ On the area of excursion sets of spherical Gaussian eigenfunctions ⋮ Ergodicity and Gaussianity for spherical random fields ⋮ Needlets Estimation in Cosmology and Astrophysics ⋮ Regression methods for testing Gaussianity on a spherical random field

Cites Work

• Graph theory applications
• On the invariance principle for nonstationary mixingales
• Correlation theory of stationary and related random functions. Volume I: Basic results
• Interpolation of spatial data. Some theory for kriging
• The empirical process on Gaussian spherical harmonics.
• Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images
• Testing for non-Gaussianity on cosmic microwave background radiation: a review.
• Nonparametric inference for the cosmic microwave background
• Bigger uncertainties and the Big Bang
• Cosmological Physics
• Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: High-resolution asymptotics for the angular bispectrum of spherical random fields