# Stein's method for nonconventional sums

## TL;DR

This paper develops a near-optimal convergence rate for the central limit theorem applied to nonconventional sums involving functions of multiple scaled indices of stochastic processes.

## Contribution

It introduces a new approach to analyze the convergence rate in the CLT for sums of the form involving multiple scaled indices, extending classical results.

## Key findings

- Established near-optimal convergence rates in the CLT for nonconventional sums.
- Extended classical CLT results to sums with multiple scaled index functions.
- Provided theoretical bounds for the convergence rate.

## Abstract

We obtain almost optimal convergence rate in the central limit theorem for "nonconevntional" sums of the form $S_N=N^{-\frac12}\sum_{n=1}^N (F(\xi_n,\xi_{2n},...,\xi_{\ell n})-\bar F)$.