Titlebook: An Invitation to Statistics in Wasserstein Space; Victor M. Panaretos,Yoav Zemel Book‘‘‘‘‘‘‘‘ 2020 The Editor(s) (if applicable) and The A

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Optimal Transport, this topic are the books by Rachev and Rüschendorf [.], Villani [., .], Ambrosio et al. [.], Ambrosio and Gigli [.], and Santambrogio [.]. This chapter includes only few proofs, when they are simple, informative, or are not easily found in one of the cited references.

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The Wasserstein Space,. The resulting metric space, a subspace of ., is commonly known as the . . (although, as Villani [., pages 118–119] puts it, this terminology is “very questionable”; see also Bobkov and Ledoux [., page 4]). In Chap. ., we shall see that this metric is in a sense canonical when dealing with warpings

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2365-4333 infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformatio978-3-030-38437-1978-3-030-38438-8Series ISSN 2365-4333 Series E-ISSN 2365-4341

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Book‘‘‘‘‘‘‘‘ 2020sures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformatio

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