A randomization test for Fréchet means in metric spaces is proposed using isotropy groups, but the proof of correct test size is left open.
Cambridge studies in advanced mathematics: Riemannian geometry: A modern introduction series number 98
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Isotropic randomization for one-sample testing in metric spaces
A randomization test for Fréchet means in metric spaces is proposed using isotropy groups, but the proof of correct test size is left open.