Estimation of the mean in partially observed branching processes with general immigration
ORCID Identifiers
Document Type
Article
Source of Publication
Statistical Inference for Stochastic Processes
Publication Date
4-15-2019
Abstract
© 2018, Springer Science+Business Media B.V., part of Springer Nature. In the paper we investigate asymptotic properties of the branching process with non-stationary immigration which are sufficient for a natural estimator of the offspring mean based on partial observations to be strongly consistent and asymptotically normal. The estimator uses only a binomially distributed subset of the population of each generation. This approach allows us to obtain results without conditions on the criticality of the process which makes possible to develop a unified estimation procedure without knowledge of the range of the offspring mean. These results are to be contrasted with the existing literature related to i.i.d. immigration case where the asymptotic normality depends on the criticality of the process and are new for the fully observed processes as well. Examples of applications in the process with immigration with regularly varying mean and variance and subcritical processes with i.i.d. immigration are also considered.
DOI Link
ISSN
Publisher
Springer Netherlands
Volume
22
Issue
1
First Page
143
Last Page
155
Disciplines
Life Sciences
Keywords
Branching process, Immigration, Limit theorems, Offspring mean, Random sum, Restricted observation
Scopus ID
Recommended Citation
Rahimov, I., "Estimation of the mean in partially observed branching processes with general immigration" (2019). All Works. 1532.
https://zuscholars.zu.ac.ae/works/1532
Indexed in Scopus
yes
Open Access
no