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On Stein factors for Laplace approximation and their application to random sums

Author

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  • Barman, Kalyan
  • Upadhye, Neelesh S.

Abstract

In this article, we consider an integral Stein equation for Laplace distribution and solve it using the semigroup approach. Next, we derive regularity estimates for the solution of the Laplace Stein equation. Finally, we apply these estimates to obtain a convergence rate for Laplace approximation of the random geometric sums. We also compare our rate with the existing literature.

Suggested Citation

  • Barman, Kalyan & Upadhye, Neelesh S., 2024. "On Stein factors for Laplace approximation and their application to random sums," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223002201
    DOI: 10.1016/j.spl.2023.109996
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    References listed on IDEAS

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    1. Robert E. Gaunt, 2020. "Wasserstein and Kolmogorov Error Bounds for Variance-Gamma Approximation via Stein’s Method I," Journal of Theoretical Probability, Springer, vol. 33(1), pages 465-505, March.
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