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Bootstrapping point processes with some applications

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  • Zarepour, M.
  • Knight, K.

Abstract

We study the weak limit behavior of certain types of point processes obtained by replacing the original observations by the bootstrap sample. The usual bootstrap fails asymptotically in cases for which there exists a Poisson point process or a fixed point measure in the limit. In some cases, by subsampling at the rate m=m(n)=o(n)-->[infinity] in the bootstrap (where n is the sample size), this problem will be resolved and convergence holds in probability. If m loglog n/n-->0 then asymptotic results are valid almost surely. The method is applied to some statistical problems.

Suggested Citation

  • Zarepour, M. & Knight, K., 1999. "Bootstrapping point processes with some applications," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 81-90, November.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:1:p:81-90
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    References listed on IDEAS

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    1. Zarepour, M., 1999. "Bootstrapping convex hulls," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 55-63, October.
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    Cited by:

    1. Mahmoud Zarepour & Thierry Bedard & Andre Dabrowski, 2008. "Return and Value at Risk using the Dirichlet Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 205-218.

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