Skip to content

Research at St Andrews

Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds

Research output: Contribution to journalArticle

Open Access Status

  • Embargoed (until 10/12/20)

Author(s)

P. E. Jupp, Alfred Kume

School/Research organisations

Abstract

The 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.
Close

Details

Original languageEnglish
JournalJournal of Multivariate Analysis
VolumeIn press
Early online date10 Dec 2019
DOIs
Publication statusE-pub ahead of print - 10 Dec 2019

    Research areas

  • Cartan-Hadamard manifold, Compositional data, Directional statistics, Exponential map, Probability integral transform, Shape space, Simplex

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Orientations of symmetrical objects

    Jupp, P. E. & Arnold, R., 2019, Applied Directional Statistics: Modern Methods and Case Studies. Ley, C. & Verdebout, T. (eds.). Boca Raton, London, New York: CRC Press, p. 25-44 20 p.

    Research output: Chapter in Book/Report/Conference proceedingChapter

  2. Bimodal or quadrimodal? Statistical tests for the shape of fault patterns

    Healy, D. & Jupp, P., 22 Aug 2018, In : Solid Earth. 9, 4, p. 1051-1060 10 p.

    Research output: Contribution to journalArticle

  3. Statistics of ambiguous rotations

    Arnold, R., Jupp, P. E. & Schaeben, H., May 2018, In : Journal of Multivariate Analysis. 165, p. 73-85

    Research output: Contribution to journalArticle

  4. A general setting for symmetric distributions and their relationship to general distributions

    Jupp, P. E., Regoli, G. & Azzalini, A., Jun 2016, In : Journal of Multivariate Analysis. 148, p. 107-119

    Research output: Contribution to journalArticle

  5. Copulae on products of compact Riemannian manifolds

    Jupp, P. E., Sep 2015, In : Journal of Multivariate Analysis. 140, p. 92-98

    Research output: Contribution to journalArticle

Related by journal

  1. Statistics of ambiguous rotations

    Arnold, R., Jupp, P. E. & Schaeben, H., May 2018, In : Journal of Multivariate Analysis. 165, p. 73-85

    Research output: Contribution to journalArticle

  2. A general setting for symmetric distributions and their relationship to general distributions

    Jupp, P. E., Regoli, G. & Azzalini, A., Jun 2016, In : Journal of Multivariate Analysis. 148, p. 107-119

    Research output: Contribution to journalArticle

  3. Copulae on products of compact Riemannian manifolds

    Jupp, P. E., Sep 2015, In : Journal of Multivariate Analysis. 140, p. 92-98

    Research output: Contribution to journalArticle

  4. Information on parameters of interest decreases under transformations

    Jupp, P. E. & Fewster, R., 2013, In : Journal of Multivariate Analysis. 120, p. 34-39 6 p.

    Research output: Contribution to journalArticle

ID: 264111141

Top