Gaussian approximations of nonlinear statistics on the sphere
  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. 
Solesne Bourguin (CMU), Claudio Durastanti (DIPMAT), Domenico   Marinucci (DIPMAT), Giovanni Peccati (FSTC)
math.PR