Statistical inference for partially observed branching processes with immigration

Author:

Rahimov Ibrahim

Abstract

AbstractIn 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.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On Transient Phenomena in Branching Random Processes with Discrete Time;Lobachevskii Journal of Mathematics;2021-12

2. Branching processes in varying environment with generation-dependent immigration;Stochastic Models;2019-03-07

3. Estimation of the mean in partially observed branching processes with general immigration;Statistical Inference for Stochastic Processes;2018-01-22

4. Bibliography;Controlled Branching Processes;2017-12-29

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