The paper derives convergence rates for two optimal transport map estimators that relax compact-support, convexity and sub-exponential tail assumptions, including a sieve estimator that drops strong convexity.
With some abuse of notation, denote ∇φ0(z) = F(z)
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Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions
The paper derives convergence rates for two optimal transport map estimators that relax compact-support, convexity and sub-exponential tail assumptions, including a sieve estimator that drops strong convexity.