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 Steins 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.
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