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

Sreenivasa Rao Jammalamadaka, Simos Meintanis, Thomas Verdebout
2020 Bernoulli  
On Sobolev tests of uniformity on the circle with an extension to the sphere Permalink https://escholarship.org/uc/item/7mb6w6k6 Journal BERNOULLI, 26(3) 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
more » ... r 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.
doi:10.3150/19-bej1191 fatcat:efeagnrexbbmnecab3pfdjsf3i