Gaussian approximations of nonlinear statistics on the sphere

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, Solé, 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.

References in corpus (2)

• Central limit theorems for $U$-statistics of Poisson point processes
• New Berry-Esseen bounds for non-linear functionals of Poisson random measures