Title

Estimation of the offspring mean in a branching process with non stationary immigration

Source of Publication

Communications in Statistics - Theory and Methods

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.

Document Type

Article

First Page

5619

Last Page

5627

Publication Date

10-1-2016

DOI

10.1080/03610926.2014.948200

Author First name, Last name, Institution

I. Rahimov, Zayed University

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