Normal Approximations for Wavelet Coefficients on Spherical Poisson Fields

Abstract

We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some results from Peccati and Zheng (2011), based on Malliavin calculus and Stein's methods, to assess the rate of convergence to Gaussianity for a triangular array of needlet coefficients with growing dimensions. Our results are motivated by astrophysical and cosmological applications, in particular related to the search for point sources in Cosmic Rays data.

28 pages

References in corpus (5)

• Central limit theorems for sequences of multiple stochastic integrals
• Central limit theorems for $U$-statistics of Poisson point processes
• Cosmological applications of a wavelet analysis on the sphere
• First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results
• Malliavin-Stein method for multi-dimensional U-statistics of Poisson point processes