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 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.
Gaussian approximation of nonlinear statistics on the sphere / Bourguin, Solesne; Durastanti, Claudio; Marinucci, Domenico; Peccati, Giovanni. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 436:2(2016), pp. 1121-1148. [10.1016/j.jmaa.2015.12.036]
Gaussian approximation of nonlinear statistics on the sphere
Durastanti, Claudio;
2016
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 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.| File | Dimensione | Formato | |
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