Nonparametric Quantile Regression: Non-Crossing Constraints and Conformal Prediction. (arXiv:2210.10161v1 [stat.ML])

We propose a nonparametric quantile regression method using deep neural
networks with a rectified linear unit penalty function to avoid quantile
crossing. This penalty function is computationally feasible for enforcing
non-crossing constraints in multi-dimensional nonparametric quantile
regression. We establish non-asymptotic upper bounds for the excess risk of the
proposed nonparametric quantile regression function estimators. Our error
bounds achieve optimal minimax rate of convergence for the Holder class, and
the prefactors of the error bounds depend polynomially on the dimension of …

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