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Poisson limits for U-statistics

Author

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  • Dabrowski, André R.
  • Dehling, Herold G.
  • Mikosch, Thomas
  • Sharipov, Olimjon

Abstract

We study Poisson limits for U-statistics with non-negative kernels. The limit theory is derived from the Poisson convergence of suitable point processes of U-statistics structure. We apply these results to derive infinite variance stable limits for U-statistics with a regularly varying kernel and to determine the index of regular variation of the left tail of the kernel. The latter is known as correlation dimension. We use the point process convergence to study the asymptotic behavior of some standard estimators of this dimension.

Suggested Citation

  • Dabrowski, André R. & Dehling, Herold G. & Mikosch, Thomas & Sharipov, Olimjon, 2002. "Poisson limits for U-statistics," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 137-157, May.
    • Handle: RePEc:eee:spapps:v:99:y:2002:i:1:p:137-157
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    References listed on IDEAS

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    1. Heinrich, L. & Wolf, W., 1993. "On the Convergence of U-Statistics with Stable Limit Distribution," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 266-278, February.
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    Cited by:

    1. Denker, M. & Kan, N., 2007. "On Sevast'yanov's theorem," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 272-279, February.
    2. Owada, Takashi, 2019. "Topological crackle of heavy-tailed moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4965-4997.

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