Poincar\'e Inequalities and Normal Approximation for Weighted Sums

TL;DR

This paper investigates bounds on how closely weighted sums of dependent variables approximate a normal distribution, using Poincaré inequalities and advanced concentration inequalities, especially in non-symmetric models.

Contribution

It extends previous normal approximation results to non-symmetric dependent models using improved concentration inequalities on high-dimensional spheres.

Findings

Derived upper bounds for Kolmogorov distance in dependent sums

Extended normal approximation results to non-symmetric models

Utilized improved concentration inequalities for sharper bounds

Abstract

Under Poincar\'e-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on improved concentration inequalities on high-dimensional Euclidean spheres, the results extend and refine previous results to non-symmetric models.