Sampling distributions and estimation for multi-type branching processes

Gonzalo Contador and Bret M. Hanlon

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 23, 7527-7552

Abstract: This study focuses on a multi-dimensional supercritical branching process with offspring distribution in a parametric family. Each vector coordinate represents the number of offspring of a given type, and the process is observed under family-size sampling: a random sample is drawn from the population, and each individual reports its vector of brood sizes. We show that the probability of no siblings being sampled (so that the sample can be considered independent) converges to one under specific conditions on the sample size. Moreover, the sampling distribution of the observations converges to a weighted mixture of offspring distributions, enabling observation to be considered an i.i.d. sample of a mixture law for which standard inference methodology applies. We provide asymptotic distributions for the resulting estimators and conduct a simulation study using respondent-driven sampling to assess their performance.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2025.2477291 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:54:y:2025:i:23:p:7527-7552

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2025.2477291

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().