Diffusion approximation of an array of controlled branching processes
type: Item
instance of: scholarly article
title: Diffusion approximation of an array of controlled branching processes
zbMATH Open document ID: 1269.60070
author: Miguel González
author: Inés M. del Puerto
published in: Methodology and Computing in Applied Probability
publication date: 2013-01-11T00:00:00Z
review text: From the authors' abstract: Controlled branching processes are considered. Using operator semigroup convergence theorems, it is proved that the fluctuation limit is a diffusion process under the conditions that the offspring and control means tend to be critical. As an application of this result, in a parametric framework, it is obtained that the bootstrapping distribution of the weighted conditional least squares estimator of the offspring mean in the critical case is not consistent. From this, it is concluded that the standard parametric bootstrap weighted conditional least squares estimate is asymptotically invalid in the critical case.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 62M05
zbMATH DE Number: 6124712
zbMATH Keywords: controlled branching processes
zbMATH Keywords: weak convergence theorem
zbMATH Keywords: diffusion processes
zbMATH Keywords: weighted conditional least squares estimation
zbMATH Keywords: parametric bootstrap
reviewed by: Alexander I. Zejfman
MaRDI profile type: Publication
full work available at URL: s11009-012-9285-8
OpenAlex ID: W2068024969
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DOI: 10.1007/S11009-012-9285-8
description: scientific article; zbMATH DE number 6124712