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A flexible soft nonlinear quantile-based regression model

Author

Listed:
  • Gholamreza Hesamian

    (Payame Noor University)

  • Arne Johannssen

    (Harz University of Applied Sciences)

  • Nataliya Chukhrova

    (University of Heidelberg)

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.

Suggested Citation

  • Gholamreza Hesamian & Arne Johannssen & Nataliya Chukhrova, 2025. "A flexible soft nonlinear quantile-based regression model," Fuzzy Optimization and Decision Making, Springer, vol. 24(1), pages 129-153, March.
    • Handle: RePEc:spr:fuzodm:v:24:y:2025:i:1:d:10.1007_s10700-025-09441-5
    DOI: 10.1007/s10700-025-09441-5
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    References listed on IDEAS

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    1. Roldán López de Hierro, Antonio Francisco & Martínez-Moreno, Juan & Aguilar Peña, Concepción & Roldán López de Hierro, Concepción, 2016. "A fuzzy regression approach using Bernstein polynomials for the spreads: Computational aspects and applications to economic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 13-25.
    2. Gholamreza Hesamian & Jalal Chachi, 2015. "Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables," Statistical Papers, Springer, vol. 56(1), pages 61-82, February.
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