Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds

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Abstract

Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Gine's Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group SO(3).

Original languageEnglish
Pages (from-to)2957-2966
Number of pages10
JournalAnnals of Statistics
Volume33
Issue number6
DOIs
Publication statusPublished - Dec 2005

Keywords

  • consistency
  • invariance
  • Riemannian manifolds
  • uniformity
  • weighted empirical distribution
  • DIRECTIONAL-DATA
  • ORIENTATION STATISTICS
  • UNIFORMITY

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