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Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration

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  • Barczy, Mátyás
  • Basrak, Bojan
  • Kevei, Péter
  • Pap, Gyula
  • Planinić, Hrvoje

Abstract

We describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton–Watson processes with regularly varying immigration with tail index α∈(1,2). The limit law is the ratio of two dependent stable random variables with indices α∕2 and 2α∕3, respectively, and it has a continuously differentiable density function. We use point process technique in the proofs.

Suggested Citation

  • Barczy, Mátyás & Basrak, Bojan & Kevei, Péter & Pap, Gyula & Planinić, Hrvoje, 2021. "Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 33-75.
    • Handle: RePEc:eee:spapps:v:132:y:2021:i:c:p:33-75
    DOI: 10.1016/j.spa.2020.10.004
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    References listed on IDEAS

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