Conformal prediction for robust deep nonparametric regression

Conformal prediction is a general method used to convert a point predictor into a prediction band. The accuracy of this prediction band is heavily reliant on the base estimator. This paper is to investigate the use of conformal prediction by least absolute deviation-based deep nonparametric regression. We demonstrate the consistency of the robust deep regression estimator under mild conditions, leading to the proposed prediction band exhibiting finite-sample marginal validity and asymptotic conditional validity. Through extensive simulation studies and a real-data example, we illustrate the benefits of conformal prediction for robust deep regression.