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Abstract
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In regression problems with multicollinearity, noise, and mixed linear–nonlinear effects, classical parametric models may suffer from instability. In this paper, we propose a semi-parametric regression framework that integrates ridgebased regularization with natural cubic spline modeling to capture smooth non-linear effects while maintaining numerical stability. The method combines the robustness of ε-insensitive support vector regression with structured ridge-type shrinkage to control model complexity and improve generalization. Empirical evaluation on the California Housing dataset demonstrates that the proposed semi-parametric support vector new ridge model outperforms competing linear and non-linear baselines in terms of predictive accuracy and information criteria, highlighting the effectiveness of combining parametric stability with spline-based flexibility.
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