  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 non-parametric 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.
