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Metrika

, Volume 32, Issue 1, pp 351–362 | Cite as

Rate of convergence to normality forU-statistics with kernel of arbitrary degree

  • M. Aerts
Publication

Summary

A recent result ofHelmers/van Zwet [1981] concerning the rate of convergence to normality forU-statistics with kernel of degree two is extended toU-statistics with kernel of arbitrary degree. At the same time, this study includes the case where, for 0<δ≤1:
$$E|h (X_1 ,...,X_r )|^p< \infty ,p > \frac{{4 + \delta }}{3},and E|g (X_1 )|^{2 + \delta }< \infty .$$

Keywords

Stochastic Process Probability Theory Economic Theory Recent Result Arbitrary Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Physica-Verlag Ges.m.b.H. 1985

Authors and Affiliations

  • M. Aerts
    • 1
  1. 1.Department of MathematicsLimburgs, Universitair CentrumDiepenbeekBelgium

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