Explicit rates of convergence in the multivariate CLT for nonlinear statistics

2018/08/24 by Nguyen Tien Dung, Dung, Nguyen Tien
Mathematics · #Advanced Statistical Methods and Models #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #math.PR

paper · pdf · doi:10.48550/arxiv.1808.08053

To appear in Acta Mathematica Hungarica, 23 pages

arxiv created 2018/11/13 · arxiv updated 2018/11/14

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.

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