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

10/03/2019

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by   Matyas Barczy, et al.

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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.