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U-max-statistics

Author

Listed:
  • Lao, W.
  • Mayer, M.

Abstract

In 1948, W. Hoeffding [W. Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Statist. 19 (1948) 293-325] introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued k-variate function h calculated at all possible sets of k points from a random sample. In the present paper, we investigate the corresponding extreme value analogue which we shall call U-max-statistics. We are concerned with the behavior of the largest value of such a function h instead of its average. Examples of U-max-statistics are the diameter or the largest scalar product within a random sample. U-max-statistics of higher degrees are given by triameters and other metric invariants.

Suggested Citation

  • Lao, W. & Mayer, M., 2008. "U-max-statistics," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2039-2052, October.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:9:p:2039-2052
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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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