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January, 1978 On Invariant Tests of Uniformity for Directions and Orientations
M. J. Prentice
Ann. Statist. 6(1): 169-176 (January, 1978). DOI: 10.1214/aos/1176344075


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 $H_3$.


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M. J. Prentice. "On Invariant Tests of Uniformity for Directions and Orientations." Ann. Statist. 6 (1) 169 - 176, January, 1978.


Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0382.62043
MathSciNet: MR458721
Digital Object Identifier: 10.1214/aos/1176344075

Primary: 62H15
Secondary: 33A45 , 33A50 , 62E15 , 62E20

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

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 1 • January, 1978
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