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

Mathematics – Statistics Theory

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Published at http://dx.doi.org/10.1214/009053605000000697 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000697

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

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