The Annals of Statistics

On Invariant Tests of Uniformity for Directions and Orientations

M. J. Prentice

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Abstract

The very general results of Beran and Gine on invariant tests of uniformity are applied to $S_p$, the surface of the unit hypersphere, and $H_p$, the surface of the unit hypersphere with antipodes identified, to give a class of invariant tests of uniformity for signed and unsigned directional data in $(p + 1)$-dimensions. The $(p + 1)$-dimensional analogues of the test statistics due to Rayleigh, Bingham, Ajne, and Gine are constructed as the simplest examples, and corresponding methods are derived for particular orientation statistics as examples on $H_3$.

Article information

Source
Ann. Statist., Volume 6, Number 1 (1978), 169-176.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344075

Digital Object Identifier
doi:10.1214/aos/1176344075

Mathematical Reviews number (MathSciNet)
MR458721

Zentralblatt MATH identifier
0382.62043

JSTOR
links.jstor.org

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62E15: Exact distribution theory 62E20: Asymptotic distribution theory 33A45 33A50

Keywords
Statistics of directions and orientations invariant tests of uniformity ultraspherical harmonics

Citation

Prentice, M. J. On Invariant Tests of Uniformity for Directions and Orientations. Ann. Statist. 6 (1978), no. 1, 169--176. doi:10.1214/aos/1176344075. https://projecteuclid.org/euclid.aos/1176344075


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Corrections

  • See Correction: M. J. Prentice. Note: Correction to "On Invariant Tests of Uniformity for Directions and Orientations". Ann. Statist., Volume 7, Number 4 (1979), 926--926.