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<p>In this paper, we propose a new inference approach designed for binary regression facing challenges such as imbalanced data, which determines the optimal predictor by leveraging Huber-type and expectile loss functions within a copula-based framework. This approach models the predictive probability of success through copulas, as investigated by Mesfioui et al. (Statistical Papers 1–29, 2023), offering greater flexibility than traditional techniques such as logistic and probit regression by transcending linear assumptions and monotonicity constraints. Unlike the method proposed by Manski and Thompson (Journal of Econometrics 40(1): 97–123 1989), which depends on the single-crossing condition, our approach relaxes this restriction and effectively captures complex, nonlinear dependencies between covariates and the response variable using copulas. Furthermore, we develop an estimator for the proposed optimal predictor based on sample data and establish the asymptotic properties of the proposed estimator. To validate the effectiveness of our method, we conduct a comprehensive simulation study and illustrate its application to real-world data, particularly in scenarios involving imbalanced datasets.</p>

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Inference Based on Copulas for Quantile and Expectile for Binary Regression

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Youssef Handi,
  • Karim Oualkacha,
  • Mhamed Mesfioui

摘要

In this paper, we propose a new inference approach designed for binary regression facing challenges such as imbalanced data, which determines the optimal predictor by leveraging Huber-type and expectile loss functions within a copula-based framework. This approach models the predictive probability of success through copulas, as investigated by Mesfioui et al. (Statistical Papers 1–29, 2023), offering greater flexibility than traditional techniques such as logistic and probit regression by transcending linear assumptions and monotonicity constraints. Unlike the method proposed by Manski and Thompson (Journal of Econometrics 40(1): 97–123 1989), which depends on the single-crossing condition, our approach relaxes this restriction and effectively captures complex, nonlinear dependencies between covariates and the response variable using copulas. Furthermore, we develop an estimator for the proposed optimal predictor based on sample data and establish the asymptotic properties of the proposed estimator. To validate the effectiveness of our method, we conduct a comprehensive simulation study and illustrate its application to real-world data, particularly in scenarios involving imbalanced datasets.