An improved test of equality of mean directions for the Langevin-von Mises-Fisher distribution

An improved test of equality of mean directions for the Langevin-von Mises-Fisher distribution

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Article ID: iaor2017848
Volume: 59
Issue: 1
Start Page Number: 119
End Page Number: 135
Publication Date: Mar 2017
Journal: Australian & New Zealand Journal of Statistics
Authors: ,
Keywords: testing, statistics: sampling, statistics: distributions
Abstract:

A multi‐sample test for equality of mean directions is developed for populations having Langevin‐von Mises‐Fisher distributions with a common unknown concentration. The proposed test statistic is a monotone transformation of the likelihood ratio. The high‐concentration asymptotic null distribution of the test statistic is derived. In contrast to previously suggested high‐concentration tests, the high‐concentration asymptotic approximation to the null distribution of the proposed test statistic is also valid for large sample sizes with any fixed nonzero concentration parameter. Simulations of size and power show that the proposed test outperforms competing tests. An example with three‐dimensional data from an anthropological study illustrates the practical application of the testing procedure.

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