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arXiv · 1910.01420

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

Matyas Barczy·Bojan Basrak·Péter Kevei·Gyula Pap·Hrvoje Planinić
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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 $\alpha \in (1,2)$. The limit law is the ratio of two dependent stable random variables with indices $\alpha/2$ and $2\alpha/3$, respectively, and it has a continuously differentiable density function. We use point process technique in the proofs.

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Matyas Barczy, Bojan Basrak, Péter Kevei, Gyula Pap, Hrvoje Planinić. 2019-10-03. Statistical inference of subcritical strongly stationary Galton--Watson processes with regularly varying immigration. https://arxiv.org/abs/1910.01420

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