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Symmetric KL-divergence by Stein’s method

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  • Yao, Liu-Quan
  • Liu, Song-Hao

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 Olnnn. The proof is based on Stein’s method. The convergence rate of order O1n and O1n are also obtained under higher moment condition.

Suggested Citation

  • Yao, Liu-Quan & Liu, Song-Hao, 2025. "Symmetric KL-divergence by Stein’s method," Stochastic Processes and their Applications, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:spapps:v:185:y:2025:i:c:s0304414925000766
    DOI: 10.1016/j.spa.2025.104635
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    References listed on IDEAS

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    1. David R. Brillinger, 1964. "Information and Information Stability of Random Variables and Processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 13(2), pages 134-135, June.
    2. M. Raič, 2004. "A Multivariate CLT for Decomposable Random Vectors with Finite Second Moments," Journal of Theoretical Probability, Springer, vol. 17(3), pages 573-603, July.
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