ONLINE - Parameter Estimation in Branching Processes with Almost Sure Extinction

16.04.2021 11:15 – 12:15

RESEARCH CENTER FOR STATISTICS SEMINAR / ABSTRACT

We consider discrete-time population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive MLEs 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 that our estimators are Q-consistent and asymptotically normal. When the offspring distribution belongs to some parametric family with unknown parameters, we show how the Q-consistent estimators can be used to obtain C-consistent least-squares estimators for the model parameters. We use our results to estimate the carrying capacity of the endangered black robin population.

Lieu

Online

entrée libre