A Stein Goodness-of-fit Test for Directional Distributions

Wenkai Xu, Takeru Matsuda
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:320-330, 2020.

Abstract

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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-xu20a, title = {A Stein Goodness-of-fit Test for Directional Distributions}, author = {Xu, Wenkai and Matsuda, Takeru}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {320--330}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/xu20a/xu20a.pdf}, url = { http://proceedings.mlr.press/v108/xu20a.html }, abstract = {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.} }
Endnote
%0 Conference Paper %T A Stein Goodness-of-fit Test for Directional Distributions %A Wenkai Xu %A Takeru Matsuda %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-xu20a %I PMLR %P 320--330 %U http://proceedings.mlr.press/v108/xu20a.html %V 108 %X 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.
APA
Xu, W. & Matsuda, T.. (2020). A Stein Goodness-of-fit Test for Directional Distributions. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:320-330 Available from http://proceedings.mlr.press/v108/xu20a.html .

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