Limit distribution theory for smooth \(p\)-Wasserstein distances

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Nonparametric statistical resampling methods (62G09)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings
Constructive quantization: approximation by empirical measures
Gaussian approximation of suprema of empirical processes
Log-concavity and strong log-concavity: a review
On the rate of convergence in Wasserstein distance of the empirical measure
\{Euclidean, metric, and Wasserstein\} gradient flows: an overview
New Donsker classes
Quantitative concentration inequalities for empirical measures on non-compact spaces
A new class of transport distances between measures
On convergence and convolutions of random signed measures
On the role of convexity in isoperimetry, spectral gap and concentration
Asymptotics for argmin processes: convexity arguments
On optimal matchings
The minimum distance method of testing
Asymptotic analysis of stochastic programs
Matching random samples in many dimensions
On nondifferentiable functions and the bootstrap
The transportation cost from the uniform measure to the empirical measure in dimension \(\geq 3\)
Asymptotics for transportation cost in high dimensions
The geometry of optimal transportation
Almost sure convergence of the minimum bipartite matching functional in Euclidean space
Isoperimetric and analytic inequalities for log-concave probability measures
A PDE approach to a 2-dimensional matching problem
Asymptotics for \(L_2\) functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances
Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
Central limit theorems for the Wasserstein distance between the empirical and the true distributions
On concepts of directional differentiability
The earth mover's distance as a metric for image retrieval
Weak convergence and empirical processes. With applications to statistics
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
A simple Fourier analytic proof of the AKT optimal matching theorem
Asymptotics of smoothed Wasserstein distances
Directional differentiability for supremum-type functionals: statistical applications
Bounds on optimal transport maps onto log-concave measures
Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces
Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications
Empirical optimal transport on countable metric spaces: distributional limits and statistical applications
On optimal matching of Gaussian samples
Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
Central limit theorems for empirical transportation cost in general dimension
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
Combinatorial Optimization Over Two Random Point Sets
Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels
The Minimum Distance Method
The geometry of logconcave functions and sampling algorithms
Mathematical Foundations of Infinite-Dimensional Statistical Models
Minimum Distance and Robust Estimation
Uniform Central Limit Theorems
Asymptotic Statistics
The Variational Formulation of the Fokker--Planck Equation
Inference for Empirical Wasserstein Distances on Finite Spaces
Inference on Directionally Differentiable Functions
Real Analysis and Probability
On parameter estimation with the Wasserstein distance
A central limit theorem for Lp transportation cost on the real line with application to fairness assessment in machine learning
Empirical Regularized Optimal Transport: Statistical Theory and Applications
Optimal Transport-Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes
Comparison between W₂ distance and Ḣ⁻¹ norm, and Localization of Wasserstein distance
The Speed of Mean Glivenko-Cantelli Convergence
Set-valued analysis
An Improved Central Limit Theorem and Fast Convergence Rates for Entropic Transportation Costs
Central limit theorems for semi-discrete Wasserstein distances
Distributionally Robust Stochastic Optimization with Wasserstein Distance