Explicit rates of convergence in the multivariate CLT for nonlinear statistics

TL;DR

This paper derives explicit convergence rates in the multivariate CLT for nonlinear statistics using Stein's method and Slepian's interpolation, with applications to Rademacher functionals, runs, and quadratic forms.

Contribution

It introduces new explicit bounds for the rate of convergence in the multivariate CLT for nonlinear statistics, utilizing difference operators and concentration inequalities.

Findings

Derived two explicit bounds for convergence rates

Applied results to Rademacher functionals and quadratic forms

Enhanced understanding of multivariate CLT for nonlinear statistics

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.