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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14943 |
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| _version_ | 1866914571021713408 |
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| author | Kuosmanen, Timo Monge, Juan F. Ruiz, José L. Zhou, Xun |
| author_facet | Kuosmanen, Timo Monge, Juan F. Ruiz, José L. Zhou, Xun |
| contents | Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key limitation of such estimators: their inability to provide meaningful marginal properties, such as shadow prices or elasticities. We propose a novel piece-wise linear smoothing framework that recovers meaningful marginal estimates even in non-convex settings. Building on the concept of conditional convexity originally developed in deterministic frontier analysis, we formulate the smoothing process as a bilevel optimization problem that fits a continuous, monotonic, piece-wise linear function to the initial isotonic regression predictions. Monte Carlo simulations demonstrate that the proposed approach can significantly improve estimation accuracy in both convex and non-convex settings for univariate and multivariate data. We apply this approach to analyze agglomeration economies in Finnish municipalities, illustrating its practical value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14943 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Piece-wise linear isotonic regression Kuosmanen, Timo Monge, Juan F. Ruiz, José L. Zhou, Xun Methodology Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key limitation of such estimators: their inability to provide meaningful marginal properties, such as shadow prices or elasticities. We propose a novel piece-wise linear smoothing framework that recovers meaningful marginal estimates even in non-convex settings. Building on the concept of conditional convexity originally developed in deterministic frontier analysis, we formulate the smoothing process as a bilevel optimization problem that fits a continuous, monotonic, piece-wise linear function to the initial isotonic regression predictions. Monte Carlo simulations demonstrate that the proposed approach can significantly improve estimation accuracy in both convex and non-convex settings for univariate and multivariate data. We apply this approach to analyze agglomeration economies in Finnish municipalities, illustrating its practical value. |
| title | Piece-wise linear isotonic regression |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.14943 |