Symmetric KL-divergence by Stein’s method

Abstract

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 order $O\left(\frac{lnn}{\sqrt{n}}\right)$. 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.