An Invitation to Statistics in Wasserstein Space

Gives a succinct introduction to necessary mathematical background, focusing on theresults useful for statistics from an otherwise vast mathematical literature.
Presents an up to date overview of the state of the art, including some original results,and discusses open problems.
Suitable for self-study or to be used as a graduate level course text.
Open access.

Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature Presents an up-to-date overview of the state of the art, including some original results,and discusses open problems Suitable for self-study or to be used as a graduate level course text

Autorentext

Prof. Victor M. Panaretos holds the Chair of Mathematical Statistics at Institute of Mathematics of the EPFL. He completed his undergraduate studies in Mathematics and Statistics in Athens and Dublin. He then received his PhD in 2007 from the University of California at Berkeley, for which he was awarded the Erich Lehmann Award. He is an Elected Member of the International Statistical Institute, a Fellow of the Institute for Mathematical Statistics, the recipient of an ERC Starting Grant Award, and was the 2019 Bernoulli Society Forum Lecturer. He serves on the editorial boards of the Annals of Statistics, Biometrika, and the Journal of the American Statistical Association.
Dr. Yoav Zemel graduated with a PhD in Mathematics at the EPFL in 2017 and is currently a postdoctoral researcher in the Statistical Laboratory at the University of Cambridge. He completed his undergraduate studies in Mathematics and Economics at the Hebrew University of Jerusalem, and earned an MSc in Applied Mathematics at the EPFL. He is the recipient of the EPFL excellence scholarship, as well as the Hebrew University Amirim scholarship, Rector's Prize and Dean's Prize.

Inhalt
Optimal transportation.- The Wasserstein space.- Fréchet means in the Wasserstein space.- Phase variation and Fréchet means.- Construction of Fréchet means and multicouplings.