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arXiv · 2610.29078

Refined Cramér-type moderate deviations by Stein's method under dependence

Hui-Lin Liu·Song-Hao Liu·Dawei Lu
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Abstract

In this paper, we establish refined Cramér-type moderate deviations for dependent random variables at any fixed order $m\geq3$. Combining higher-order Stein identities with exponential tilting, we obtain cumulant-corrected tail approximations with explicit error bounds for boundedly supported kernels. Our main application gives a fourth-order expansion under bounded local dependence, reaching an $O(n^{3/10})$ deviation range under standard normalization with fixed dependence parameters. It improves on previous work in both deviation range and applicability, and also covers bounded $m$-dependent sequences without an independent-base representation. Further applications to the generalized combinatorial central limit theorem and the Curie-Weiss model also extend some earlier results under permutation and mean-field dependence.

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Hui-Lin Liu, Song-Hao Liu, Dawei Lu. 2026-10-21. Refined Cramér-type moderate deviations by Stein's method under dependence. https://arxiv.org/abs/2610.29078

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