Dai, Sheng, Kuosmanen, Timo and Zhou, Xun orcid.org/0000-0003-2093-4508 (2022) Partial frontiers are not quantiles. [Preprint]
Abstract
Quantile regression and partial frontier are two distinct approaches to nonparametric quantile frontier estimation. In this article, we demonstrate that partial frontiers are not quantiles. Both convex and nonconvex technologies are considered. To this end, we propose convexified order-α as an alternative to convex quantile regression (CQR) and convex expectile regression (CER), and two new nonconvex estimators: isotonic CQR and isotonic CER as alternatives to order-α. A Monte Carlo study shows that the partial frontier estimators perform relatively poorly and even can violate the quantile property, particularly at low quantiles. In addition, the simulation evidence shows that the indirect expectile approach to estimating quantiles generally outperforms the direct quantile estimations. We further find that the convex estimators outperform their nonconvex counterparts owing to their global shape constraints. An illustration of those estimators is provided using a real-world dataset of U.S. electric power plants.
Metadata
Item Type: | Preprint |
---|---|
Authors/Creators: |
|
Dates: |
|
Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Environment and Geography (York) |
Depositing User: | Pure (York) |
Date Deposited: | 08 Jun 2023 23:18 |
Last Modified: | 16 Oct 2024 11:41 |
Published Version: | https://doi.org/10.48550/arXiv.2205.11885 |
Status: | Published |
Publisher: | arXiv |
Identification Number: | 10.48550/arXiv.2205.11885 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200229 |