Power of Tests of Uniformity Defined on the Hypersphere

Figueiredo, Adelaide; Gomes, Paulo

doi:10.1081/sac-120013113

Cited by 8 publications

(5 citation statements)

References 4 publications

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“…Let us switch to a comparative Monte Carlo power study of proposed uniformity criteria. N -distance tests with strongly negative definite kernel L(x, y) = x − y are compared with classical criteria: Rayleigh (R) [3,4], Watson (W) [5,6], Giné (G) [3] and Ajne (A) [7,8] for circular S 1 and spherical S 2 cases.…”

Section: Empirical Power Resultsmentioning

confidence: 99%

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N-distance tests of uniformity on the hypersphere

Bakshaev¹

2010

NAMC

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Section: Empirical Power Resultsmentioning

confidence: 99%

“…Several invariant tests for uniformity of a distribution on the circle, the sphere and the hemisphere have been proposed by Rayleigh [3,4], Watson [5,6], Ajne [7], Beran [8] and others. In this paper we propose an application of N -distance theory for testing the hypothesis of uniformity of spherical data.…”

Section: Introductionmentioning

confidence: 99%

N-distance tests of uniformity on the hypersphere

Bakshaev¹

2010

NAMC

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“…Related with (viii), studied the powers of Ajne and Watson tests under the Rt alternative with t = 1/2 and different values of κ, finding that Ajne was only barely more powerful (see his Table 3). With respect to (ix ), Figueiredo and Gomes (2003) compared the Bingham and Giné's G n tests under different dimensions, sample sizes, and concentrations, finding no remarkable differences between them (see their Table 3). Figueiredo (2007) conducted a similar analysis for the Rayleigh and Ajne tests with identical conclusions (see her Tables 2-4).…”

Section: Ad {B Admentioning

confidence: 99%

On a projection-based class of uniformity tests on the hypersphere

García‐Portugués¹,

Navarro-Esteban²,

Cuesta-Albertos³

2020

Preprint

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We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the projected data and the projected uniform distribution. Simple expressions for several test statistics are obtained for the circle and sphere, and relatively tractable forms for higher dimensions. Despite its different origin, the proposed class is shown to be related with the well-studied Sobolev class of uniformity tests. Our new class proves itself advantageous by allowing to derive new tests for hyperspherical data that neatly extend the circular tests by Watson, Ajne, and Rothman, and by introducing the first instance of an Anderson-Darling-like test for such data. The asymptotic distributions and the local optimality against certain alternatives of the new tests are obtained. A simulation study evaluates the theoretical findings and evidences that, for certain scenarios, the new tests are competitive against previous proposals. The new tests are employed in three astronomical applications.

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“…The following are more topic-specific recommendations. Comparative simulation studies between uniformity tests are available in Stephens (1969a), Diggle et al (1985), Figueiredo andGomes (2003), andFigueiredo (2007). Comparisons of test efficiencies are given in Shepherd and Rao (1970), Rao…”

Section: Further Readingmentioning

confidence: 99%

An overview of uniformity tests on the hypersphere

García-Portugués,

Verdebout

2018

Preprint

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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 notable particular cases, some recent alternative tests, and novel results in the highdimensional low-sample size case. A reasonably comprehensive bibliography on the topic is provided.

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Power of Tests of Uniformity Defined on the Hypersphere

Cited by 8 publications

References 4 publications

N-distance tests of uniformity on the hypersphere

N-distance tests of uniformity on the hypersphere

On a projection-based class of uniformity tests on the hypersphere

An overview of uniformity tests on the hypersphere

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