Isotonic, trend filtering, and ReLU network distributional regression estimators achieve CRPS and worst-case MSE rates matching the corresponding mean-regression rates, uniformly over thresholds.
Sharp oracle inequalities for least squares estimators in shape restricted regression.The Annals of Statistics, 46(2):745–780, 2018
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Risk Bounds For Distributional Regression
Isotonic, trend filtering, and ReLU network distributional regression estimators achieve CRPS and worst-case MSE rates matching the corresponding mean-regression rates, uniformly over thresholds.