Gaussian approximations of nonlinear statistics on the sphere
Probability
2017-12-20 v1
Abstract
We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of -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.
Cite
@article{arxiv.1407.6584,
title = {Gaussian approximations of nonlinear statistics on the sphere},
author = {Solesne Bourguin and Claudio Durastanti and Domenico Marinucci and Giovanni Peccati},
journal= {arXiv preprint arXiv:1407.6584},
year = {2017}
}