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dc.contributor.authorJupp, P. E.
dc.contributor.authorKume, Alfred
dc.identifier.citationJupp , P E & Kume , A 2020 , ' Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds ' , Journal of Multivariate Analysis , vol. 176 , 104579 .
dc.identifier.otherPURE: 264111141
dc.identifier.otherPURE UUID: 3fe178ce-7e82-415e-a6b6-a8f072a9660a
dc.identifier.otherORCID: /0000-0003-0973-8434/work/66069886
dc.identifier.otherScopus: 85076700942
dc.identifier.otherWOS: 000509418400008
dc.description.abstractThe standard method of transforming a continuous distribution on the line to the uniform distribution on [0,1 ]is the probability integral transform. Analogous transforms exist on compact Riemannian manifolds, X, in that for each distribution with continuous positive density on X, there is a continuous mapping of X to itself that transforms the distribution into the uniform distribution. In general, this mapping is far from unique. This paper introduces the construction of an almost-canonical version of such a probability integral transform. The construction is extended to shape spaces, Cartan–Hadamard manifolds, and simplices. The probability integral transform is used to derive tests of goodness of fit from tests of uniformity. Illustrative examples of these tests of goodness of fit are given involving (i) Fisher distributions on S2, (ii) isotropic Mardia–Dryden distributions on the shape space Σ52 Their behaviour is investigated by simulation.
dc.relation.ispartofJournal of Multivariate Analysisen
dc.rightsCopyright © 2019 Elsevier Inc. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at
dc.subjectCartan-Hadamard manifolden
dc.subjectCompositional dataen
dc.subjectDirectional statisticsen
dc.subjectExponential mapen
dc.subjectProbability integral transformen
dc.subjectShape spaceen
dc.subjectQA Mathematicsen
dc.titleMeasures of goodness of fit obtained by almost-canonical transformations on Riemannian manifoldsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.description.statusPeer revieweden

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