Title

Estimation of the mean in partially observed branching processes with general immigration

Author First name, Last name, Institution

I. Rahimov, Zayed University

ORCID Identifiers

0000-0003-0733-1147

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.

ISSN

1387-0874

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

85040773455

Indexed in Scopus

yes

Open Access

no

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