Statistical inference for partially observed branching processes with immigration

Ibrahim Rahimov, Zayed University

Document Type

Article

Source of Publication

Journal of Applied Probability

Publication Date

3-1-2017

Abstract

Copyright © 2017 Applied Probability Trust. In the paper we consider the following modification of a discrete-time branching process with stationary immigration. In each generation a binomially distributed subset of the population will be observed. The number of observed individuals constitute a partially observed branching process. After inspection both observed and unobserved individuals may change their offspring distributions. In the subcritical case we investigate the possibility of using the known estimators for the offspring mean and for the mean of the stationary-limiting distribution of the process when the observation of the population sizes is restricted. We prove that, if both the population and the number of immigrants are partially observed, the estimators are still strongly consistent. We also prove that the 'skipped' version of the estimator for the offspring mean is asymptotically normal and the estimator of the stationary distribution's mean is asymptotically normal under additional assumptions.

ISSN

0021-9002

Publisher

Cambridge University Press

Volume

54

Issue

1

First Page

82

Last Page

95

Disciplines

Life Sciences

Keywords

Branching process, immigration, limit theorem, offspring mean, random sum, restricted observation, stationary distribution, subcritical

Scopus ID

85017144219

Indexed in Scopus

yes

Open Access

no

Link to Full Text

Share

COinS