Modified likelihood ratio test for homogeneity in a mixture of von Mises distributions

Directional data are often collected in applications such as in genetics, geology and astrolomy. One particular statistical problem of interest is whether the data are from a mixture of two von Mises distributions or a single von Mises distribution. Motivating examples including a DNA microarray experiment where it is suggested that a proportion of circadian genes have systematically different phase/peak expressions in two different tissues. We study the use of modified likelihood ratio test (MLRT) to this class of problems. The MLRT statistic is shown to have a simple χ1 null limiting distribution. The result is extended to general parametric kernels. The simulation study gives additional insight into the finite-sample performance of the test. For illustration, two real data examples are also given.