A flexible soft nonlinear quantile-based regression model

• Verfasst von: Hesamian, Gholamreza [VerfasserIn]
• Verfasst von: Johannssen, Arne [VerfasserIn]
• Verfasst von: Chukhrova, Nataliya [VerfasserIn]
• Titel: A flexible soft nonlinear quantile-based regression model
• Verf.angabe: Gholamreza Hesamian, Arne Johannssen, Nataliya Chukhrova
• E-Jahr: 2025
• Jahr: March 2025
• Umfang: 25 S.
• Illustrationen: Illustrationen
• Fussnoten: Online veröffentlicht: 6. März 2025 ; Gesehen am 14.07.2025
• Titel Quelle: Enthalten in: Fuzzy optimization and decision making
• Ort Quelle: Dordrecht [u.a.] : Springer Science + Business Media B.V., 2002
• Jahr Quelle: 2025
• Band/Heft Quelle: 24(2025), 1, Seite 129-153
• ISSN Quelle: 1573-2908
• DOI: doi:10.1007/s10700-025-09441-5
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Cross-validation
• Sach-SW: Econometrics
• Sach-SW: Explainability
• Sach-SW: Financial Econometrics
• Sach-SW: Fuzzy quantiles
• Sach-SW: Fuzzy regression
• Sach-SW: Kernel-fitting
• Sach-SW: Least absolute errors
• Sach-SW: Parametric Inference
• Sach-SW: Quantitative Economics
• Sach-SW: Quantitative Finance
• Sach-SW: Robustness
• Sach-SW: Statistical Finance
• K10plus-PPN: 1930443560

Abstract

There are several models for soft regression analysis in the literature, but relatively few are based on quantiles, and these models are limited to the linear case. As quantile-based regression models offer a series of benefits (like robustness and handling of asymmetric distributions) but have not been considered in the nonlinear case, we present the first soft nonlinear quantile-based regression model in this paper. Considering nonlinearity instead of limiting to linearity in the modeling brings numerous advantages such as a higher flexibility, more accurate predictions, a better model fit and an improved explainability/interpretability of the model. In particular, we embed fuzzy quantiles into nonlinear regression analysis with crisp predictor variables and fuzzy responses. We propose a new method for parameter estimation by implementing a three-stage technique on the basis of the center and the spreads. In the framework of this procedure, we utilize kernel-fitting, a least quantile loss function, least absolute errors, and generalized cross-validation criteria to estimate the model parameters. We perform comprehensive comparative analysis with other soft nonlinear regression models that have demonstrated superiority in previous studies. The results reveal that the proposed nonlinear quantile-based regression technique leads to better outcomes compared to the competitors.