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

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

  • M. Aerts


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:
$$E|h (X_1 ,...,X_r )|^p< \infty ,p > \frac{{4 + \delta }}{3},and E|g (X_1 )|^{2 + \delta }< \infty .$$


Stochastic Process Probability Theory Economic Theory Recent Result Arbitrary Degree 
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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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