Jagath Senarathne | Searcharxiv

arXiv2026

A Copula-Based Regression Framework for Enhanced Prediction under Heteroscedasticity

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.

stat.ME↗

arXiv2026

Improving Linear Regression on Small Datasets via Gaussian Process and Extreme Value Theory-Based Data Augmentation

Small sample sizes pose significant challenges in regression analysis, often leading to violations of classical assumptions such as normality, homoscedasticity, and independence of residuals. These violations compromise parameter estimation accuracy, reduce statistical power, and limit the generalizability of findings. This study introduces the Gaussian Process-based Modified Extreme Value Theorem (GP-MEVT) method, a novel hybrid data augmentation approach that combines Gaussian Process with Extreme Value Theory to address these limitations. The GP-MEVT method generates augmented observations that extend the predictor space beyond the observed range while preserving the underlying linear structure and introducing controlled variability based on residual variation, through comprehensive simulation studies across three variance scenarios (sigma = 2, 5, 8) and sample sizes (n = 10, 15, 20). Here, we demonstrate that GP-MEVT achieves a higher rate of assumption satisfaction, substantially outperforming standard bootstrap and bootstrap with noise methods. The proposed method also exhibits reasonable parameter estimation accuracy, with intercept and slope estimates consistently closer to true parameter values, and maintains competitive or superior model fitting performance as measured by root mean square error. Application to a real-world dataset confirms these advantages, with GP-MEVT achieving a 67.1% assumption satisfaction rate compared to 17.3% and 21.2% for bootstrap alternatives. These findings establish GP-MEVT as a robust and reliable framework for fitting linear regression models to small datasets, offering practitioners a principled approach to statistical inference when sample size limitations are unavoidable.

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