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

I. Rahimov ()
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I. Rahimov: Zayed University

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 1, No 6, 143-155

Abstract: Abstract 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.

Keywords: Branching process; Immigration; Restricted observation; Offspring mean; Random sum; Limit theorems; Primary 60J80; Secondary 62F12; 60G99 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11203-017-9170-8

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