Inference on the common mean direction of several Fisher-von Mises-Langevin populations with unknown concentration parameters

The problem of combining information from several samples for estimating or testing a common mean for normal populations has been extensively studied in the statistical literature. In this paper, we take up this problem in the context of the common mean direction of several Fisher-von Mises-Langevin (FvML) distributions. The concentration parameters are taken to be unknown and heterogeneous. A non-iterative combined estimator is proposed and is seen to have substantially better risk performance than individual sample mean directions and a grand mean direction in a simulation study. Further, a test based on this non-iterative estimator is proposed, and nonparametric bootstrap and permutation resampling methods are developed for its implementation. Two more alternative tests are proposed and their implementation is carried out using nonparametric bootstrap resampling. A detailed simulation study shows that these test procedures achieve the nominal size and have good power performance. An 'R' package is developed for the implementation of the tests. A real data set is considered for illustrating the procedures.