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Elements of Statistical Inference in 2-Wasserstein Space

  • Johannes EbertEmail author
  • Vladimir Spokoiny
  • Alexandra Suvorikova
Conference paper
Part of the CIM Series in Mathematical Sciences book series (CIMSMS)

Abstract

This work addresses an issue of statistical inference for the datasets lacking underlying linear structure, which makes impossible the direct application of standard inference techniques and requires a development of a new tool-box taking into account properties of the underlying space.We present an approach based on optimal transportation theory that is a convenient instrument for the analysis of complex data sets. The theory originates from seminal works of a french mathematician Gaspard Monge published at the end of 18th century. This chapter recalls the basics on optimal transportations theory, explains the ideas behind statistical inference on non-linear manifolds, and as an illustrative example presents a novel approach of construction of non asymptotic confidence sets for so calledWasserstein barycenter, a generalized analogous of Euclidean mean to the case of non-linear space endowed with a particular distance belonging to a class of Earth-Mover distances that it is a main object of study in optimal transportation theory. The chapter is based on the paper [18].

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Johannes Ebert
    • 1
    Email author
  • Vladimir Spokoiny
    • 2
  • Alexandra Suvorikova
    • 3
  1. 1.Humboldt University of BerlinBerlinGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  3. 3.Potsdam UniversityPotsdamGermany

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