Normal approximations for wavelet coefficients on spherical Poisson fields
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- 作者：Claudio Durastanti ; Domenico Marinucci ; Giovanni Peccati
- 关键词：Berry&ndash ; Esseen bounds ; Malliavin calculus ; Multidimensional normal approximation ; Poisson process ; Stein&rsquo ; s method ; Spherical wavelets
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2014
- 出版时间：1 January, 2014
- 年：2014
- 卷：409
- 期：1
- 页码：212-227
- 全文大小：472 K
文摘
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) , 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.