Adaptive tests for ANOVA in Fisher–von Mises–Langevin populations under heteroscedasticity

Fisher–von Mises–Langevin distributions are widely used for modeling directional data. In this paper, the problem of testing homogeneity of mean directions of several Fisher–von Mises–Langevin populations is considered when the concentration parameters are unknown and heterogeneous. First, an adaptive test based on the likelihood ratio statistic is proposed. Critical points are evaluated using a parametric bootstrap. Second, a heuristic test statistic is considered based on pairwise group differences. A nonparametric bootstrap procedure is adapted for evaluating critical points. Finally, a permutation test is also proposed. An extensive simulation study is performed to compare the size and power values of these tests with those proposed earlier. It is observed that both parametric and nonparametric bootstrap based tests achieve size values quite close to the nominal size. Asymptotic tests and permutation tests have size values higher than the nominal size. Bootstrap tests are seen to have very good power performance. The robustness of tests is also studied by considering contamination in Fisher–von Mises–Langevin distributions. R packages are developed for the actual implementation of all tests. A real data set has been considered for illustrations.