# A Stein Goodness-of-fit Test for Directional Distributions

arXiv: https://arxiv.org/abs/2002.06843 · HTML: https://mlsanity.com/paper/2002.06843/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2020.

## Built on by (most cited first, 13 of 13)

- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [A kernel Stein test of goodness of fit for sequential models](https://mlsanity.com/paper/2210.10741/) (2022)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generators](https://mlsanity.com/paper/2203.03673/) (2022)
- [The Minimax Lower Bound of Kernel Stein Discrepancy Estimation](https://mlsanity.com/paper/2510.15058/) (2025)
- [Expanding SPHERE-JEPA: A Family of Statistical Regularizers for the Hypersphere](https://mlsanity.com/paper/2606.17603/) (2026)
- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)
- [Kernel Tests of Equivalence](https://mlsanity.com/paper/2603.10886/) (2026)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Sequential Kernelized Stein Discrepancy](https://mlsanity.com/paper/2409.17505/) (2024)

## Abstract (arXiv)

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.