The Annals of Statistics
- Ann. Statist.
- Volume 6, Number 1 (1978), 169-176.
On Invariant Tests of Uniformity for Directions and Orientations
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 $H_3$.
Ann. Statist., Volume 6, Number 1 (1978), 169-176.
First available in Project Euclid: 12 April 2007
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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
- 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.