Central limit theorems for empirical transportation cost in general dimension
By Eustasio del Barrio, Jean-Michel Loubes. Annals of Probability, 2017
119 citations recorded by the source corpus.
We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We provide new results on the uniqueness and stability of the associated optimal transportation potentials , namely, the minimizers in the dual formulation of the optimal transportation problem. As a consequence, we show that a CLT holds for the empirical transportation cost under mild moment and smoothness requirements. The limiting distributions are Gaussian and admit a simple description in terms of the optimal transportation potentials.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/7b18773fc7fc816cfb2d80e0727e34c4c034eb97
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In Applied Mathematics
- Marc Hallin
- Eustasio del Barrio
- Gilles Mordant
- Johan Segers
- Vladimir Spokoiny
- Alexandra L. Suvorikova
- Alexey Kroshnin
- Juan Antonio Cuesta-Albertos
Citations in the corpus
- Statistical inference for Bures–Wasserstein barycenters (2019, methodology): “, Goodnight and Schwartz [1997], Calsbeek and Goodnight [2009], Álvarez-Esteban et al.”
- Multivariate goodness-of-fit tests based on Wasserstein distance (2020, background): “Important advances on the limit distribution have been made by del Barrio and Loubes (2019) who obtained results under fixed alternatives.”
- Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications (2017, background): “In the case of finite X conditions for S∗(r, s) to be a singleton are known (Hung et al., 1986; Klee and Witzgall, 1968). d) Parallel to our work del Barrio and Loubes (2017) showed asymptotic normality of EWD in general dimensions for the case r 6= s.”
- Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, methodology): “The tools we are using throughout are exploiting the concept of cyclical monotonicity and the approach initiated by McCann (1995).(7) Section 4 provides some numerical results.”