Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds
The Annals of Statistics · 2005 · Volume 33 · Issue 6
DOI: 10.1214/009053605000000697
Abstract
Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Giné’s Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group SO(3).
Keywords
62F03, 62F05, 62H11, consistency, Invariance, Riemannian manifolds, uniformity, weighted empirical distribution
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