Sobolev Tests of Goodness of Fit of Distributions on Compact Riemannian Manifolds

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).

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Veröffentlicht in:	The Annals of statistics 2005-12, Vol.33 (6), p.2957-2966
1. Verfasser:	Jupp, P. E.
Format:	Artikel
Sprache:	eng
Schlagworte:	62F03 62F05 62H11 Consistency Density distributions Exact sciences and technology Gin Goodness of fit Goodness of Fit Tests invariance Mathematical models Mathematics Multivariate analysis Null hypothesis Parametric inference Probabilities Probability and statistics Riemann manifold Riemannian manifolds Sciences and techniques of general use Statistical analysis Statistical theories Statistics Studies Theorems Uniformity weighted empirical distribution
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Zusammenfassung:	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).
ISSN:	0090-5364 2168-8966
DOI:	10.1214/009053605000000697