Asymptotic inference for non-supercritical partially observed branching processes

I. Rahimov, Zayed University

Document Type

Article

Source of Publication

Statistics and Probability Letters

Publication Date

7-1-2017

Abstract

© 2017 Elsevier B.V. To estimate the offspring mean of a branching process one needs observed population sizes up to some generation. However, in applications very often not all individuals existing in the population are observed. Therefore the question about possibility of estimating the population mean based on partial observations is of interest. In existing literature this problem has been studied assuming that the process never becomes extinct, which is possible only in supercritical case. In the paper we consider it in subcritical and critical processes with a large number of initial ancestors. We prove that the Harris type ratio estimator remains consistent, if we have observations of a binomially distributed subsets of the population. To obtain the asymptotic normality of the estimator we modify the estimator using a “skipping” method. The proofs use the law of large numbers and the central limit theorem for random sums in the case when the number of terms and the terms in the sum are not independent.

ISSN

0167-7152

Publisher

Elsevier B.V.

Volume

126

First Page

26

Last Page

32

Disciplines

Life Sciences

Keywords

Branching process, Limit theorems, Offspring mean, Random sum, Restricted observation

Scopus ID

85014828633

Indexed in Scopus

yes

Open Access

no

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