A comparison of some conformal quantile regression methods

We compare two recent methods that combine conformal inference with quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano, Patterson, & Candès, 2019, arXiv:1905.03222; Kivaranovic, Johnson, & Leeb, 2019, arXiv:1905.10634). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method of Romano et al. typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization. Our empirical results suggest that using between 70% and 90% of the data for training often achieves a good balance between minimizing the average width of the predictions intervals and the variability in their practical coverage.