Abstract: Fisher-von Mises-Langevin (FvML) distribution is one of the most widely used directional distributions for modeling and analyzing directional data. This work deals with the testing for the homogeneity of the mean directions of several FvML populations when the concentration parameters are unknown and unequal. We consider several adaptive test procedures, viz., a parametric bootstrap based likelihood ratio test, a contrast based nonparametric bootstrap test and a permutation test. Algorithms for computation of critical points, size and power values are given. We present empirical size and power comparison results for different test procedures for various configurations of the concentration parameters, sample sizes and number of groups. These are also compared with the empirical size and power values of certain tests existing in literature. Robustness of the proposed tests is also investigated under contaminated FvML distributions. ‘R’ packages are developed for implementation of all procedures and these are further illustrated on areal data set.

Speaker Bio: Dr. Shreyashi Basak is an Assistant Professor in the Department of Mathematics, BITS Pilani, K K Birla Goa Campus. Her research interests include statistical inference, computer vision, deep learning, and statistical analysis.