# An overview of uniformity tests on the hypersphere

@article{GarciaPortugues2018AnOO, title={An overview of uniformity tests on the hypersphere}, author={Eduardo Garc'ia-Portugu'es and Thomas Verdebout}, journal={arXiv: Methodology}, year={2018} }

When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different from uniformity. We review in this article a reasonably exhaustive collection of uniformity tests for assessing uniformity in the hypersphere. Specifically, we review the classical circular-specific tests, the large class of Sobolev tests with its many…

## 12 Citations

On Sobolev tests of uniformity on the circle with an extension to the sphere

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- 2020

Circular and spherical data arise in many applications, especially in Biology, Earth Sciences and Astronomy. In dealing with such data one of the preliminary steps before any further inference, is to…

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Testing uniformity on the $p$-dimensional unit sphere is arguably the most fundamental problem in directional statistics. In this paper, we consider this problem in the framework of axial data, that…

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We consider one of the most classical problems in multivariate statistics, namely the problem of testing isotropy, or equivalently, the problem of testing uniformity on the unit hypersphere Sp−1 of…

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A lower bound on the minimax separation rate is derived and it is established that the Bingham test is minimax rate-optimal in the class of Watson distributions.

A Stein Goodness-of-fit Test for Directional Distributions

- MathematicsAISTATS
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This study proposes non-parametric goodness-of-fit testing procedures for general directional distributions based on kernel Stein discrepancy based on Stein's operator on spheres, which is derived by using Stokes' theorem.

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- MathematicsJ. Multivar. Anal.
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Data-driven stabilizations of goodness-of-fit tests

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Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null…

A Cramér–von Mises Test of Uniformity on the Hypersphere

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- 2020

Testing uniformity of a sample supported on the hypersphere is one of the first steps when analysing multivariate data for which only the directions (and not the magnitudes) are of interest. In this…

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