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

Peter Edmund Jupp

doi:10.1214/009053605000000697

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

Peter Edmund Jupp

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	2957-2966
Number of pages	10
Journal	Annals of Statistics
Volume	33
Issue number	6
DOIs	https://doi.org/10.1214/009053605000000697
Publication status	Published - Dec 2005

Keywords

consistency
invariance
Riemannian manifolds
uniformity
weighted empirical distribution
DIRECTIONAL-DATA
ORIENTATION STATISTICS
UNIFORMITY

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10.1214/009053605000000697

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title = "Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds",

abstract = "Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Gine'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 = "consistency, invariance, Riemannian manifolds, uniformity, weighted empirical distribution, DIRECTIONAL-DATA, ORIENTATION STATISTICS, UNIFORMITY",

author = "Jupp, {Peter Edmund}",

year = "2005",

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KW - consistency

KW - invariance

KW - Riemannian manifolds

KW - uniformity

KW - weighted empirical distribution

KW - DIRECTIONAL-DATA

KW - ORIENTATION STATISTICS

KW - UNIFORMITY

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JO - Annals of Statistics

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ER -

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

Abstract

Keywords

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