U-statistics based on the Green's function of the Laplacian on the circle and the sphere

  • Pycke J
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Abstract

We show that the Watson and Cramér-von Mises statistics are related to Green's function of the Laplacian on a circle. A generalization leads to a new U-statistic whose kernel is the Green function of the Laplacian on the sphere. © 2007 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Anderson-Darling statistic
  • Cramér-von Mises statistic
  • Directional statistics
  • Tests of uniformity
  • U- and V-statistics
  • Watson statistic

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Authors

  • J. R. Pycke

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