Explicit rates of convergence in the multivariate CLT for nonlinear statistics
Probability
2018-11-14 v2
Abstract
We investigate the multivariate central limit theorem for nonlinear statistics by means of Stein's method and Slepian's smart path interpolation method. Based on certain difference operators in theory of concentration inequalities, we obtain two explicit bounds for the rate of convergence. Applications to Rademacher functionals, the runs and quadratic forms are provided as well.
Cite
@article{arxiv.1808.08053,
title = {Explicit rates of convergence in the multivariate CLT for nonlinear statistics},
author = {Nguyen Tien Dung},
journal= {arXiv preprint arXiv:1808.08053},
year = {2018}
}
Comments
To appear in Acta Mathematica Hungarica, 23 pages