A note on the regularity of optimal-transport-based center-outward distribution and quantile functions

DOI10.1016/j.jmva.2020.104671zbMath1450.62047OpenAlexW3081694290MaRDI QIDQ2201563

Marc Hallin, Alberto González Sanz, Eustasio del Barrio

Publication date: 29 September 2020

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2020.104671

zbMATH Keywords

Monge-Ampère equationoptimal transportationmultivariate ranksquantile contours

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Nonparametric regression and quantile regression (62G08) Functional data analysis (62R10) Nonparametric robustness (62G35) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Convergence of probability measures (60B10) Monge-Ampère equations (35J96)

Related Items

Center-Outward R-Estimation for Semiparametric VARMA Models ⋮ Multivariate ranks and quantiles using optimal transport: consistency, rates and nonparametric testing ⋮ Efficient Fully Distribution-Free Center-Outward Rank Tests for Multiple-Output Regression and MANOVA ⋮ On some connections between Esscher's tilting, saddlepoint approximations, and optimal transportation: a statistical perspective ⋮ Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biology ⋮ Central limit theorems for semi-discrete Wasserstein distances ⋮ Functional, randomized and smoothed multivariate quantile regions ⋮ Distribution and quantile functions, ranks and signs in dimension \(d\): a measure transportation approach ⋮ On universally consistent and fully distribution-free rank tests of vector independence ⋮ Rank-based testing for semiparametric VAR models: a measure transportation approach

Uses Software

• MNM

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