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dc.contributor.authorJupp, P. E.
dc.contributor.authorKume, Alfred
dc.date.accessioned2020-12-10T00:37:16Z
dc.date.available2020-12-10T00:37:16Z
dc.date.issued2020-03
dc.identifier264111141
dc.identifier3fe178ce-7e82-415e-a6b6-a8f072a9660a
dc.identifier85076700942
dc.identifier000509418400008
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 . https://doi.org/10.1016/j.jmva.2019.104579en
dc.identifier.issn0047-259X
dc.identifier.otherORCID: /0000-0003-0973-8434/work/66069886
dc.identifier.urihttps://hdl.handle.net/10023/21127
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.format.extent486025
dc.language.isoeng
dc.relation.ispartofJournal of Multivariate Analysisen
dc.subjectCartan-Hadamard manifolden
dc.subjectCompositional dataen
dc.subjectDirectional statisticsen
dc.subjectExponential mapen
dc.subjectProbability integral transformen
dc.subjectShape spaceen
dc.subjectSimplexen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
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.identifier.doi10.1016/j.jmva.2019.104579
dc.description.statusPeer revieweden
dc.date.embargoedUntil2020-12-10


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