The authors construct prediction intervals by calibrating estimated conditional CDF values on a grid, and show asymptotic validity for DNN and kernel estimators, with a finite-sample coverage guarantee only under an oracle DNN assumption.
Nonparametric estimation of smooth conditional distributions
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Calibration Prediction Interval for Non-parametric Regression and Neural Networks
The authors construct prediction intervals by calibrating estimated conditional CDF values on a grid, and show asymptotic validity for DNN and kernel estimators, with a finite-sample coverage guarantee only under an oracle DNN assumption.