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

Research output: Contribution to journalArticle

Standard

Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds. / Jupp, P. E.; Kume, Alfred.

In: Journal of Multivariate Analysis, Vol. In press, 10.12.2019.

Research output: Contribution to journalArticle

Harvard

Jupp, PE & Kume, A 2019, 'Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds', Journal of Multivariate Analysis, vol. In press. https://doi.org/10.1016/j.jmva.2019.104579

APA

Jupp, P. E., & Kume, A. (2019). Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds. Journal of Multivariate Analysis, In press. https://doi.org/10.1016/j.jmva.2019.104579

Vancouver

Jupp PE, Kume A. Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds. Journal of Multivariate Analysis. 2019 Dec 10;In press. https://doi.org/10.1016/j.jmva.2019.104579

Author

Jupp, P. E. ; Kume, Alfred. / Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds. In: Journal of Multivariate Analysis. 2019 ; Vol. In press.

Bibtex - Download

@article{3fe178ce7e82415ea6b6a8f072a9660a,
title = "Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds",
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.",
keywords = "Cartan-Hadamard manifold, Compositional data, Directional statistics, Exponential map, Probability integral transform, Shape space, Simplex",
author = "Jupp, {P. E.} and Alfred Kume",
year = "2019",
month = dec,
day = "10",
doi = "10.1016/j.jmva.2019.104579",
language = "English",
volume = "In press",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds

AU - Jupp, P. E.

AU - Kume, Alfred

PY - 2019/12/10

Y1 - 2019/12/10

N2 - 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.

AB - 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.

KW - Cartan-Hadamard manifold

KW - Compositional data

KW - Directional statistics

KW - Exponential map

KW - Probability integral transform

KW - Shape space

KW - Simplex

U2 - 10.1016/j.jmva.2019.104579

DO - 10.1016/j.jmva.2019.104579

M3 - Article

VL - In press

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -

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ID: 264111141

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