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Estimation of the mean for critical branching process and its bootstrap approximation

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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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Acknowledgments

The authors would like to thank an anonymous referee for pointing out some errors in the previous version, as well as for many valuable comments that have led to the improvements in this work. This research is supported by Natural Science Foundation of China (No. 11201421); Humanities & Social Science Foundation of Ministry of Education of China (No. 10YJC910010); Natural Science Foundation of Zhejiang Province (No. LY12A01020, No. LQ12A01018 & No. Y6110110); Foundation for Young Talents of ZJGSU (No. 1020XJ1311015).

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Authors and Affiliations

  1. College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Xiao-Rong Yang

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  1. Xiao-Rong Yang
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Correspondence to Xiao-Rong Yang.

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Yang, XR. Estimation of the mean for critical branching process and its bootstrap approximation. Metrika 76, 831–846 (2013). https://doi.org/10.1007/s00184-012-0418-4

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  • DOI: https://doi.org/10.1007/s00184-012-0418-4

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