The needlets bispectrum

DOI10.1214/08-EJS197zbMath1320.62106arXiv0802.4020MaRDI QIDQ1951752

Xiaohong Lan, Domenico Marinucci

Publication date: 24 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.4020

zbMATH Keywords

spherical random fieldsneedletsbispectrumcosmic microwave background radiationhigh resolution asymptotics

Mathematics Subject Classification ID

Random fields (60G60) Random fields; image analysis (62M40) Asymptotic properties of nonparametric inference (62G20) Inference from stochastic processes and spectral analysis (62M15) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (17)

Separable projection integrals for higher-order correlators of the cosmic microwave sky: acceleration by factors exceeding 100 ⋮ Adaptive global thresholding on the sphere ⋮ Localisation of directional scale-discretised wavelets on the sphere ⋮ Mixed needlets ⋮ Spin wavelets on the sphere ⋮ Needlet-Whittle estimates on the unit sphere ⋮ Spin needlets spectral estimation ⋮ Adaptive nonparametric regression on spin fiber bundles ⋮ Spectral estimation on the sphere with needlets: high frequency asymptotics ⋮ Gaussian semiparametric estimates on the unit sphere ⋮ On the limiting behaviour of needlets polyspectra ⋮ On the dependence structure of wavelet coefficients for spherical random fields ⋮ Statistical challenges in the analysis of cosmic microwave background radiation ⋮ Asymptotic uncorrelation for Mexican needlets ⋮ Needlets Estimation in Cosmology and Astrophysics ⋮ Asymptotic behaviour of level sets of needlet random fields ⋮ Block thresholding on the sphere

Uses Software

• Healpix

Cites Work

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• Subsampling needlet coefficients on the sphere
• Group representations and high-resolution central limit theorems for subordinated spherical random fields
• Decomposition of Besov and Triebel-Lizorkin spaces on the sphere
• Some characterizations of the spherical harmonics coefficients for isotropic random fields
• A central limit theorem for generalized multilinear forms
• A central limit theorem and higher order results for the angular bispectrum
• Practical wavelet design on the sphere
• Asymptotics for spherical needlets
• Wavelets on the two-sphere and other conic sections
• Complex data processing: Fast wavelet analysis on the sphere
• Cosmological applications of a wavelet analysis on the sphere
• Needlet algorithms for estimation in inverse problems
• High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus
• High-resolution asymptotics for the angular bispectrum of spherical random fields
• Central limit theorems for sequences of multiple stochastic integrals
• Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
• Localized Tight Frames on Spheres
• GAUSS–LEGENDRE SKY PIXELIZATION (GLESP) FOR CMB MAPS
• Random Fields and Geometry

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