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Berry–Esseen bound and Cramér-type moderate deviations of the maximum likelihood estimator in Rayleigh diffusion process

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  • Wen, Minhan
  • Guan, Ruoning
  • Jiang, Hui

Abstract

In this paper, we consider the asymptotic properties of the maximum likelihood estimator of the drift coefficient in the Rayleigh diffusion process. Via the parameter-dependent change of measure method and precise asymptotic analysis techniques, we obtain the optimal Cramér-type moderate deviations and uniform Berry–Esseen bound.

Suggested Citation

  • Wen, Minhan & Guan, Ruoning & Jiang, Hui, 2026. "Berry–Esseen bound and Cramér-type moderate deviations of the maximum likelihood estimator in Rayleigh diffusion process," Statistics & Probability Letters, Elsevier, vol. 231(C).
    • Handle: RePEc:eee:stapro:v:231:y:2026:i:c:s0167715225002731
    DOI: 10.1016/j.spl.2025.110628
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    References listed on IDEAS

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    1. Nenghui Kuang & Fuqing Gao, 2014. "Hypothesis Testing in a Rayleigh Diffusion Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(9), pages 1907-1917, May.
    2. Cui, Jiazhen & Liu, Qiaojing, 2023. "Cramér-type moderate deviations for the log-likelihood ratio of inhomogeneous Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 192(C).
    3. Qi-Man Shao, 1999. "A Cramér Type Large Deviation Result for Student's t-Statistic," Journal of Theoretical Probability, Springer, vol. 12(2), pages 385-398, April.
    4. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2008. "Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 209-217.
    5. Zani, Marguerite, 2002. "Large deviations for squared radial Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 25-42, November.
    6. Zhao, Shoujiang & Liu, Qiaojing, 2020. "A large deviation result for maximum likelihood estimator of non-homogeneous Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 162(C).
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