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

P.E. Jupp and A. Kume

Journal of Multivariate Analysis, 2020, vol. 176, issue C

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.

Keywords: Cartan–Hadamard manifold; Compositional data; Directional statistics; Exponential map; Probability integral transform; Shape space; Simplex (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.jmva.2019.104579

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