Name: Symmetric KL-divergence by Stein’s method
Keywords: Probability (math.PR), central limit theorem, FOS: Mathematics, Central limit and other weak theorems, Stein's method, symmetric KL-divergence, Mathematics - Probability, 60F05, 60G50

Symmetric KL-divergence by Stein's method

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2025Embargo end date: 01 Jan 2024 English Publisher:Elsevier BVJournal:Stochastic Processes and their Applications, volume 185, page 104,635 (issn: 0304-4149,

Authors: Yao, Liu-Quan; Liu, Song-Hao;

doi: 10.1016/j.spa.2025.104635 , 10.48550/arxiv.2401.11381

arXiv: http://arxiv.org/abs/2401.11381

Symmetric KL-divergence by Stein’s method

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Abstract

In this paper, we consider the symmetric KL-divergence between the sum of independent variables and a Gaussian distribution, and obtain a convergence rates of order $O\left( \frac{\ln n}{\sqrt{n}}\right)$. 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.

33 pages

Keywords

Probability (math.PR), central limit theorem, FOS: Mathematics, Central limit and other weak theorems, Stein's method, symmetric KL-divergence, Mathematics - Probability, 60F05, 60G50

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