Information Geometry of Wasserstein Statistics on Shapes and Affine Deformations

arXiv:2307.12508v4 Announce Type: replace-cross
Abstract: Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework of Li and Zhao (2023) for the affine deformation statistical model, which is a multi-dimensional generalization of the location-scale model. We compare merits and demerits of estimators based on information geometry and Wasserstein geometry. The shape of a probability distribution and its affine deformation …

abstract arxiv framework geometry information manifold math.st probability replace statistical statistics stat.ml stat.th study type