The Annals of Statistics

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

P. E. Jupp

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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 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).

Article information

Source
Ann. Statist., Volume 33, Number 6 (2005), 2957-2966.

Dates
First available in Project Euclid: 17 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1140191680

Digital Object Identifier
doi:10.1214/009053605000000697

Mathematical Reviews number (MathSciNet)
MR2253109

Zentralblatt MATH identifier
1085.62065

Subjects
Primary: 62F03: Hypothesis testing 62F05: Asymptotic properties of tests 62H11: Directional data; spatial statistics

Keywords
Consistency invariance Riemannian manifolds uniformity weighted empirical distribution

Citation

Jupp, P. E. Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds. Ann. Statist. 33 (2005), no. 6, 2957--2966. doi:10.1214/009053605000000697. https://projecteuclid.org/euclid.aos/1140191680


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