Partial frontiers are not quantiles
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908579693330432 |
|---|---|
| author | Dai, Sheng Kuosmanen, Timo Zhou, Xun |
| author_facet | Dai, Sheng Kuosmanen, Timo Zhou, Xun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11885 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Partial frontiers are not quantiles Dai, Sheng Kuosmanen, Timo Zhou, Xun Methodology Applications 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. |
| title | Partial frontiers are not quantiles |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2205.11885 |