 Bootstrap of the offspring mean in the critical process with a non-stationary immigrationI. Rahimov Stochastic Processes and their Applications, 2009, vol. 119, issue 11, 3939-3954 Abstract: In applications of branching processes, usually it is hard to obtain samples of a large size. Therefore, a bootstrap procedure allowing inference based on a small sample size is very useful. Unfortunately, in the critical branching process with stationary immigration the standard parametric bootstrap is invalid. In this paper, we consider a process with non-stationary immigration, whose mean and variance vary regularly with nonnegative exponents [alpha] and [beta], respectively. We prove that 1+2[alpha] is the threshold for the validity of the bootstrap in this model. If [beta] 1+2[alpha] it is invalid. In the case [beta]=1+2[alpha], the validity of the bootstrap depends on the slowly varying parts of the immigration mean and variance. These results allow us to develop statistical inferences about the parameters of the process in its early stages. Keywords: Branching; process; Non-stationary; immigration; Parametric; bootstrap; Threshold; Martingale; theorem; Skorokhod; space (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:spapps:v:119:y:2009:i:11:p:3939-3954 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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