Estimation of the offspring mean in a branching process with non stationary immigration
Document Type
Article
Source of Publication
Communications in Statistics - Theory and Methods
Publication Date
10-1-2016
Abstract
© 2016, © Taylor & Francis Group, LLC. In the paper, we consider a natural estimator of the offspring mean of a branching process with non stationary immigration based on observation of population sizes and number of immigrating individuals to each generation. We demonstrate that using a central limit theorem for multiple sums of dependent random variables it is possible to derive asymptotic distributions for the estimator without prior knowledge about the behavior (criticality) of the reproduction process. Before the three cases of criticality have been considered separately. Assuming that the immigration mean and variance vary regularly, conditions guaranteeing the strong consistency of the proposed estimator is also derived.
DOI Link
ISSN
Publisher
Taylor and Francis Inc.
Volume
45
Issue
19
First Page
5619
Last Page
5627
Disciplines
Life Sciences
Keywords
Branching process, Consistency, Generation-dependent immigration, Natural estimator, Offspring mean, Random sum
Scopus ID
Recommended Citation
Rahimov, I., "Estimation of the offspring mean in a branching process with non stationary immigration" (2016). All Works. 1533.
https://zuscholars.zu.ac.ae/works/1533
Indexed in Scopus
yes
Open Access
no