A study on the consistency of estimators for population-size-dependent branching processes with almost sure extinction

P. Braunsteins, S. Hautphenne, C. Minuesa Abril

In this presentation, we examine population-size-dependent branching processes (PSDBPs), which are stochastic models that describe the evolution of populations living in environments with limited resources.

Our research focuses on PSDBPs in which extinction is certain. Within a parametric framework for the offspring distributions, we address the problem of estimating the model parameters. Based on the sample of the population sizes in each generation, we propose a new weighted least-squares estimator. We establish its C-consistency and its convergence to a normal distribution once it is suitably normalised. Additionally, we show the advantages of the new estimator by investigating the relationship between the new and the classic least-squares estimators and the differences in their performances via a simulation study.

Palabras clave: branching process, almost sure extinction, weighted least-squares estimator, consistency

Procesos Estocásticos y sus aplicaciones II
12 de junio de 2025  15:30
Auditorio 2. Leandre Cristòfol

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