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We describe the asymptotic behavior of the conditional least squaresestimator of the offspring mean for subcritical strongly stationaryGalton--Watson processes with regularly varying immigration with tail index$\alpha \in (1,2)$. The limit law is the ratio of two dependent stable randomvariables with indices $\alpha/2$ and $2\alpha/3$, respectively, and it has acontinuously differentiable density function. We use point process technique inthe proofs.

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