# E-Statistics, Group Invariance and Anytime Valid Testing

@inproceedings{PerezOrtiz2022EStatisticsGI, title={E-Statistics, Group Invariance and Anytime Valid Testing}, author={Muriel Felipe P'erez-Ortiz and Tyron Lardy and Rianne de Heide and Peter D. Grunwald}, year={2022} }

We study worst-case growth-rate optimal (GROW) e -statistics for hypothesis testing between two group models. If the underlying group G acts freely on the observation space, there exists a maximally invariant statistic of the data. We show that among all e -statistics, invariant or not, the likelihood ratio of the maximally invariant is GROW and that an anytime valid test can be based on this likelihood ratio. By virtue of a representation theorem of Wijsman, it is equivalent to a Bayes factor…

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