Parameter estimation in branching processes with almost sure extinction

P Braunsteins; S Hautphenne; C Minuesa

Journal article

Parameter estimation in branching processes with almost sure extinction

P Braunsteins, S Hautphenne, C Minuesa

Bernoulli | Published : 2021

DOI: 10.3150/21-BEJ1332

Abstract

We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when the current population size is z ≥ 1. As is standard in branching process theory, an asymptotic analysis of the estimators requires us to condition on non-extinction up to a finite generation n and let n → ∞; however, because the processes become extinct with probability one, we are able to demonstrate that our estimators do not satisfy the classical consistency property (C-consistency). This leads us to define the concept of Q-consistency, and we prove th..

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University of Melbourne Researchers

Sophie Hautphenne Author

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Grants

Awarded by Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers

Funding Acknowledgements

Peter Braunsteins has conducted part of the work while supported by the Australian Research Council (ARC) Laureate Fellowship FL130100039 and the Netherlands Organisation for Scientific Research (NWO) through Gravitation-grant NETWORKS-024.002.003. Sophie Hautphenne would like to thank the Australian Research Council (ARC) for support through her Discovery Early Career Researcher Award DE150101044 and her Discovery Project DP200101281. Carmen Minuesa's research has been supported by the Ministerio de Economia y Competitividad (grant MTM2015-70522-P) , the Span-ish State Research Agency (PID2019-108211GBI00/AEI/10.13039/501100011033) , the Junta de Ex-tremadura (grants IB16099 and GR18103) and the Fondo Europeo de Desarrollo Regional. This re-search was initiated while Carmen Minuesa was a visiting postdoctoral researcher at The University of Melbourne, and she is grateful for the hospitality and collaboration. She also acknowledges the ARC Centre of Excellence for Mathematical and Statistical Frontiers for partially supporting her research visit at this University. Finally, the authors thank the anonymous referees for their valuable comments.