An evaluation by simulation of alternative estimators for the marginal Fisher distribution

The Fisher distribution is a standard model for directional data (or spherical data). In some cases though, only the co-latitudes can be observed, resulting in a sample of observations from the corresponding marginal distribution. This paper reports on an extensive simulation to compare and evaluate the robustness of 11 test-statistics corresponding to various estimators of the parameters of this distribution. The estimators include Maximum Likelihood and Moment-type estimators, as well as sample means and variances based on approximations to the marginal Fisher distribution. Of the test-statistics considered, the Likelihood-Ratio statistic was the only one whose sampling distribution remained close to its asymptotic distribution for all parameter values and sample sizes considered. In general, the other statistics were close to their approximate distributions only when ksin2?0, was fairly large. The paper includes details on the computational methods for finding the Maximum Likelihood and Moment estimators, and concludes with some practical advice on the choice of estimation procedure.