We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelet/needlet coefficients based on a homogeneous spherical Poisson field. In particular, we develop some results from Peccati and Zheng (2010) [42], 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.
Durastanti, C., Marinucci, D., Peccati, G. (2014). Normal approximations for wavelet coefficients on spherical Poisson fields. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 409(1), 212-227 [10.1016/j.jmaa.2013.06.028].
Normal approximations for wavelet coefficients on spherical Poisson fields
MARINUCCI, DOMENICO;
2014-01-01
Abstract
We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelet/needlet coefficients based on a homogeneous spherical Poisson field. In particular, we develop some results from Peccati and Zheng (2010) [42], 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.File | Dimensione | Formato | |
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