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A large sample property in approximating the superposition of i.i.d. finite point processes

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  • Cong, Tianshu
  • Xia, Aihua
  • Zhang, Fuxi

Abstract

One of the main differences between the central limit theorem and the Poisson law of small numbers is that the former possesses the large sample property (LSP), i.e., the error of normal approximation to the sum of n independent identically distributed (i.i.d.) random variables converges to 0 as n→∞. Since 1980s, considerable effort has been devoted to recovering the LSP for the law of small numbers in discrete random variable approximation. In this paper, we aim to establish the LSP for the superposition of i.i.d. finite point processes.

Suggested Citation

  • Cong, Tianshu & Xia, Aihua & Zhang, Fuxi, 2020. "A large sample property in approximating the superposition of i.i.d. finite point processes," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4493-4511.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:7:p:4493-4511
    DOI: 10.1016/j.spa.2020.01.006
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    References listed on IDEAS

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    1. Barbour, A. D. & Utev, Sergey, 1999. "Compound Poisson approximation in total variation," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 89-125, July.
    2. Schuhmacher, Dominic, 2005. "Distance estimates for dependent superpositions of point processes," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1819-1837, November.
    3. Brown, Timothy C. & Weinberg, Graham V. & Xia, Aihua, 2000. "Removing logarithms from Poisson process error bounds," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 149-165, May.
    4. Xia, Aihua & Zhang, Fuxi, 2008. "A polynomial birth-death point process approximation to the Bernoulli process," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1254-1263, July.
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