• Corpus ID: 88523748

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… 
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12 Citations
Background Citations
5
Methods Citations
4
Results Citations
1

12 Citations

Citation Type

Citation Type

On Sobolev tests of uniformity on the circle with an extension to the sphere
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…
On the power of axial tests of uniformity on spheres
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…
On the power of Sobolev tests for isotropy under local rotationally symmetric alternatives
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…
Testing uniformity on high-dimensional spheres: The non-null behaviour of the Bingham test
TLDR
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
TLDR
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.
The Statistics of Circular Optimal Transport
Empirical optimal transport (OT) plans and distances provide effective tools to compare and statistically match probability measures defined on a given ground space. Fundamental to this are…
Harmonic analysis and distribution-free inference for spherical distributions
Data-driven stabilizations of goodness-of-fit tests
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…
On some multivariate sign tests for scatter matrix eigenvalues
A Cramér–von Mises Test of Uniformity on the Hypersphere
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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References

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