 Asymptotic inference for non-supercritical partially observed branching processesI. Rahimov Statistics & Probability Letters, 2017, vol. 126, issue C, 26-32 Abstract: 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. Keywords: Branching process; Restricted observation; Offspring mean; Random sum; Limit theorems (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:126:y:2017:i:c:p:26-32 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2017.02.024 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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