Abstract
This article focuses attention on the estimation of the mean of a sequence of branching process with immigration in the critical case. We get the limiting distribution of the pivot, and adopt a bootstrap procedure to bootstrap the least-square estimator with bootstrap sample size \(m\) less than the size \(n\) of the original sample. Under the assumptions that \(m\rightarrow \infty \) and \(m/n\rightarrow 0\), the convergence in probability of the bootstrap distribution function is also established.
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