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

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 is an element of (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. (C) 2020 The Author(s). Published by Elsevier B.V.

Automated summary

This paper focuses on the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton-Watson processes with regularly varying immigration. The limit law is the ratio of two dependent stable random variables with specific indices, and it has a continuously differentiable density function. Point process technique is used in the proofs.