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Poisson convergence for set-indexed empirical processes

Author

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  • Ivanoff, B. Gail
  • Merzbach, Ely

Abstract

A compensator associated with a set-indexed single jump process is computed. This leads to a direct construction of a compensator associated with a set-indexed empirical process, where a family of i.i.d. random variables is given in a Euclidean space. It is then shown that if the distribution function is differentiable at the origin, the suitably resealed empirical process converges to a spatial Poisson process.

Suggested Citation

  • Ivanoff, B. Gail & Merzbach, Ely, 1997. "Poisson convergence for set-indexed empirical processes," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 81-86, February.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:1:p:81-86
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    References listed on IDEAS

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    1. Mazziotto, Gerald & Merzbach, Ely, 1988. "Point processes indexed by directed sets," Stochastic Processes and their Applications, Elsevier, vol. 30(1), pages 105-119, November.
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    Cited by:

    1. Borisov, I. S., 2000. "A note on Poisson approximation of rescaled set-indexed empirical processes," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 101-103, January.

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