Empirical Bayes estimation in directional data

Empirical Bayes procedures have been developed extensively in the literature, under the assumption that the underlying parameter space (or the sample space) is Euclidean in nature. However, there has been almost no research carried out into when the data comes from a different space. We develop empirical Bayes techniques to estimate the mean direction of the Fisher-von Mises distribution. In this case, the underlying space is non-Euclidean. The special case when the data are angles on the unit circle is illustrated with an example.