Regularity of center-outward distribution functions in non-convex domains

Directional data; spatial statistics (62H11) Nonparametric robustness (62G35) Transportation, logistics and supply chain management (90B06) Convergence of probability measures (60B10) Optimal transportation (49Q22)

Cites Work

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The Monge-Ampère equation and its applications
Monge-Kantorovich depth, quantiles, ranks and signs
Boundary regularity of maps with convex potentials. II
A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
Partial regularity of Brenier solutions of the Monge-Ampère equation
On the continuity of center-outward distribution and quantile functions
Existence and uniqueness of monotone measure-preserving maps
Distribution and quantile functions, ranks and signs in dimension \(d\): a measure transportation approach
On the regularity of optimal transports between degenerate densities
A note on the regularity of optimal-transport-based center-outward distribution and quantile functions
Regularity of monotone transport maps between unbounded domains
Semiparametrically efficient rank-based inference for shape. I: optimal rank-based tests for sphericity
Multivariate quantiles and multiple-output regression quantiles: from \(L_{1}\) optimization to halfspace depth
Central limit theorems for empirical transportation cost in general dimension
Local bilinear multiple-output quantile/depth regression
Characterization of the subdifferentials of convex functions
Sharp boundary \(\varepsilon\)-regularity of optimal transport maps
The Regularity of Mappings with a Convex Potential
Some regularity properties of solutions of Monge Ampère equation
Boundary regularity of maps with convex potentials
Variational Analysis
Convex Analysis
Regularity properties of monotone measure-preserving maps
Central limit theorems for general transportation costs

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