A Stein Goodness-of-fit Test for Directional Distributions

In many fields, data appears in the form of direction (unit vector) and usual statistical procedures are not applicable to such directional data. In this study, we propose nonparametric goodness-of-fit testing procedures for general directional distributions based on kernel Stein discrepancy. Our method is based on Stein’s operator on spheres, which is derived by using Stokes’ theorem. Notably, the proposed method is applicable to distributions with an intractable normalization constant, which commonly appear in directional statistics. Experimental results demonstrate that the proposed methods control type-I error well and have larger power than existing tests, including the test based on the maximum mean discrepancy.