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August 2020 On Sobolev tests of uniformity on the circle with an extension to the sphere
Sreenivasa Rao Jammalamadaka, Simos Meintanis, Thomas Verdebout
Bernoulli 26(3): 2226-2252 (August 2020). DOI: 10.3150/19-BEJ1191


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 test if such data is isotropic, that is, uniformly distributed around the circle or the sphere. In view of its importance, there is a considerable literature on the topic. In the present work, we provide new tests of uniformity on the circle based on original asymptotic results. Our tests are motivated by the shape of locally and asymptotically maximin tests of uniformity against generalized von Mises distributions. We show that they are uniformly consistent. Empirical power comparisons with several competing procedures are presented via simulations. The new tests detect particularly well multimodal alternatives such as mixtures of von Mises distributions. A practically-oriented combination of the new tests with already existing Sobolev tests is proposed. An extension to testing uniformity on the sphere, along with some simulations, is included. The procedures are illustrated on a real dataset.


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Sreenivasa Rao Jammalamadaka. Simos Meintanis. Thomas Verdebout. "On Sobolev tests of uniformity on the circle with an extension to the sphere." Bernoulli 26 (3) 2226 - 2252, August 2020.


Received: 1 April 2019; Revised: 1 December 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193958
MathSciNet: MR4091107
Digital Object Identifier: 10.3150/19-BEJ1191

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability


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Vol.26 • No. 3 • August 2020
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