## The Annals of Statistics

### On Invariant Tests of Uniformity for Directions and Orientations

M. J. Prentice

#### 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