# Stein's method via induction

## TL;DR

This paper introduces an inductive approach to Stein's method that effectively handles non-bounded variables with complex dependencies, providing optimal rate bounds for normal approximation in new applications.

## Contribution

It develops a novel inductive technique for Stein's method that applies to non-bounded couplings and demonstrates its effectiveness on complex dependent structures.

## Key findings

- Achieved Berry-Esseen bounds for Erdős-Rényi graphs with fixed edges.
- Applied to Jack measure on tableaux, showing method's versatility.
- Produced bounds in Kolmogorov metric with optimal rate.

## Abstract

Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two applications, one to the Erd\H{o}s-R\'enyi, random graph with a fixed number of edges, and one to Jack measure on tableaux, demonstrate that the method can handle non-bounded variables with non-trivial global dependence, and can produce bounds in the Kolmogorov metric with the optimal rate.