Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.
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Presents a drift transformation framework for multidimensional diffusions that yields product-form transition densities, with explicit results for Wiener and Ornstein-Uhlenbeck cases including resetting and stochastic ordering.
An optimal transport method is proposed to construct confidence intervals with improved coverage, including theoretical consistency results, error bounds, and simulation comparisons.
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Wasserstein Least Squares: A Canonical Regression Method for Probability Distributions
Wasserstein least squares extends Euclidean least squares to distribution-valued responses via convex analysis, yielding n^{-1/2} rates under template deformation and faster barycenter rates than prior work.