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arXiv · 1407.6584

Gaussian approximations of nonlinear statistics on the sphere

Solesne Bourguin·Claudio Durastanti·Domenico Marinucci·Giovanni Peccati
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Abstract

We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of $U$-statistics, built from wavelets coefficients evaluated on a homogeneous spherical Poisson field of arbitrary dimension. For this purpose, we exploit the Stein-Malliavin approach introduced in the seminal paper by Peccati, Sol\'e, Taqqu and Utzet (2011); we focus in particular on statistical applications covering evaluation of variance in non-parametric density estimation and Sobolev tests for uniformity.

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Solesne Bourguin, Claudio Durastanti, Domenico Marinucci, Giovanni Peccati. 2014-07-24. Gaussian approximations of nonlinear statistics on the sphere. https://arxiv.org/abs/1407.6584

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