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Limiting Distributions for the Maximum of a Symmetric Function on a Random Point Set

Author

Listed:
  • M. J. Appel

    (Mortgage Guaranty Insurance Corporation)

  • R. P. Russo

    (University of Iowa)

Abstract

Let U 1, U 2, ... be a sequence of independent random points taking values in a measurable space (S, Σ) according to a common probability P and let $$h:S\times S\rightarrow$$ R be a symmetric, Borel/ $$\Sigma\times\Sigma$$ -measurable function. Let H n = max{h(U i ,U j ): 1≤ i

Suggested Citation

  • M. J. Appel & R. P. Russo, 2006. "Limiting Distributions for the Maximum of a Symmetric Function on a Random Point Set," Journal of Theoretical Probability, Springer, vol. 19(2), pages 365-375, June.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:2:d:10.1007_s10959-006-0013-6
    DOI: 10.1007/s10959-006-0013-6
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    References listed on IDEAS

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    1. Henze, Norbert & Klein, Timo, 1996. "The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 228-239, May.
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    Cited by:

    1. Tang, Ping & Lu, Rongrong & Xie, Junshan, 2022. "Asymptotic distribution of the maximum interpoint distance for high-dimensional data," Statistics & Probability Letters, Elsevier, vol. 190(C).

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