Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces

DOI10.3150/19-BEJ1151zbMath1455.60009arXiv1804.10556MaRDI QIDQ2278679

Jing Lei

Publication date: 5 December 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.10556

zbMATH Keywords

empirical processconcentration inequalityempirical measureWasserstein distancefunctional data

Mathematics Subject Classification ID

Gaussian processes (60G15) Inequalities; stochastic orderings (60E15) Order statistics; empirical distribution functions (62G30) Convergence of probability measures (60B10) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (13)

Minimax confidence intervals for the sliced Wasserstein distance ⋮ Measure estimation on manifolds: an optimal transport approach ⋮ Randomized Wasserstein Barycenter Computation: Resampling with Statistical Guarantees ⋮ Convergence rates for empirical measures of Markov chains in dual and Wasserstein distances ⋮ Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks ⋮ On the capacity of deep generative networks for approximating distributions ⋮ Stein Variational Gradient Descent on Infinite-Dimensional Space and Applications to Statistical Inverse Problems ⋮ Sharp convergence rates for empirical optimal transport with smooth costs ⋮ Uniform confidence band for optimal transport map on one-dimensional data ⋮ Local continuity of log-concave projection, with applications to estimation under model misspecification ⋮ A second order analysis of McKean-Vlasov semigroups ⋮ Network representation using graph root distributions ⋮ Measuring dependence between random vectors via optimal transport

Uses Software

• Wasserstein GAN

Cites Work

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