Robustness of tests for directional mean

We compute the level and power breakdown properties of the three test functionals and compare them. We find that the circular trimmed mean test functional has the best robustness properties for both the above-mentioned distributions.

The level and power properties of the test statistics corresponding to these functionals are also studied. Two examples with real data are given for illustration. We also consider the problem of testing the mean direction of the von-Mises–Fisher distribution on the unit sphere and explore the robustness properties of the spherical mean direction and likelihood ratio test functionals.