一种基于Copula的回归框架用于异方差下的增强预测

中文摘要 AI 辅助

经典回归方法，如普通最小二乘法，依赖残差恒定方差和正态性等强假设，而实际数据常违反这些假设。尽管对数变换常用于稳定方差，但可能引入反变换偏差且无法充分解决异方差和不对称依赖结构。本研究提出基于Copula的回归框架来处理存在异方差误差结构的数据。该方法明确考虑异方差，无需严格分布假设。通过综合模拟研究比较其与常用回归模型和对数线性模型的性能。模拟结果表明，基于Copula的模型始终优于传统方法，在真实数据应用中也进一步证实了其有效性，证明其在存在异方差和复杂依赖结构时是一种可行的建模选择。

英文摘要

Classical regression approaches, including ordinary least squares, rely on strong assumptions such as constant variance and normality of residuals, which are often violated in real-world data. Although log-transformation is commonly used to stabilise variance, it may introduce re-transformation bias and fail to address heteroscedasticity and asymmetric dependence structures adequately. To overcome these limitations, this study proposes a copula-based regression framework for modelling data in the presence of heteroscedastic error structures. The proposed copula-based regression framework separates marginal distributions of the response and explanatory variables from their dependence structure, allowing flexible modelling of different tail-dependent relationships. The proposed approach explicitly accounts for heteroscedasticity without requiring restrictive distributional assumptions. A comprehensive simulation study and two real-world applications were considered under heteroscedastic scenarios to compare the performance of the proposed method with existing methods. The simulation results demonstrated that the proposed copula-based model consistently outperformed conventional approaches, achieving an average mean absolute percentage error of 0.21, compared with 0.27 and 0.36 for the linear and log-linear models, respectively. In the first application, which exhibited clear heteroscedasticity, the copula-based model achieved the lowest MAPE, although the overall differences between the copula-based and GAMLSS models were not substantial. In Application 2, all models achieved low predictive performance, as there was a moderate linear relationship between the response and predictor variables. Overall, the findings indicate that no single model consistently dominates across all settings, while copula-based regression provides a flexible and competitive alternative for heteroscedastic data.

发表机构

• Postgraduate Institute of Science, University of Peradeniya（佩拉德尼亚大学研究生科学学院）
• Department of Computer Science and Statistics, University of Peradeniya（佩拉德尼亚大学计算机科学与统计系）

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