Optimal inference for circular variation diminishing experiments with applications to the von-Mises distribution and the Fisher-Efron parabola model

Abstract.

Complete classes and optimal tests for variation diminishing circular distributions are constructed. This is applied to inference for the mean direction of a von Mises distributed r.v. whenever the concentration parameter κ≤½. Similar results are shown for the cardioid and multimodal von-Mises family. Furthermore, our result reinforces the shape of the locally admissible tests for the mean of a bivariate normal r.v. as it was found by Brown & Marden (1992) for the Fisher-Efron parabola model. We find that this test is conditionally optimal whenever the Fisher-information of the experiment is not too large.