Symmetric KL-divergence by Stein's Method

Liu-Quan Yao, Song-Hao Liu

Published 2024-01-21Version 1

In this paper, we consider the symmetric KL-divergence between the sum of independent variables and a Gaussian distribution, and obtain a convergence rate of $O\left( \frac{\ln n}{\sqrt{n}}\right)$. The proof is based on Stein's method. The convergence rate of order $O\left( \frac{1}{\sqrt{n}}\right)$ and $O\left( \frac{1}{n}\right) $ are also obtained under higher moment condition.