Title

Statistical inference for partially observed branching processes with immigration

Source of Publication

Journal of Applied Probability

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.

Document Type

Article

First Page

82

Last Page

95

Publication Date

3-1-2017

DOI

10.1017/jpr.2016.88

Author First name, Last name, Institution

Ibrahim Rahimov, Zayed University

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