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

P. E. Jupp

doi:10.1214/009053605000000697

paper

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

arXiv:math/0603135 · 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 $SO (3)$ .

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