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Cramér moderate deviations for a supercritical Galton–Watson process

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  • Doukhan, Paul
  • Fan, Xiequan
  • Gao, Zhi-Qiang

Abstract

Let (Zn)n≥0 be a supercritical Galton–Watson process. The Lotka–Nagaev estimator Zn+1/Zn is a common estimator for the offspring mean. In this paper, we establish some Cramér moderate deviation results for the Lotka–Nagaev estimator via a martingale method. Applications to construction of confidence intervals are also given.

Suggested Citation

  • Doukhan, Paul & Fan, Xiequan & Gao, Zhi-Qiang, 2023. "Cramér moderate deviations for a supercritical Galton–Watson process," Statistics & Probability Letters, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:stapro:v:192:y:2023:i:c:s0167715222002243
    DOI: 10.1016/j.spl.2022.109711
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    References listed on IDEAS

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    1. Liuyan Li & Junping Li, 2021. "Large Deviation Rates for Supercritical Branching Processes with Immigration," Journal of Theoretical Probability, Springer, vol. 34(1), pages 162-172, March.
    2. Grama, Ion & Liu, Quansheng & Miqueu, Eric, 2017. "Berry–Esseen’s bound and Cramér’s large deviation expansion for a supercritical branching process in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1255-1281.
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    5. Fan, Xiequan & Grama, Ion & Liu, Quansheng & Shao, Qi-Man, 2020. "Self-normalized Cramér type moderate deviations for stationary sequences and applications," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5124-5148.
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