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Abstract
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This paper introduces a new penalized parametric regression estimator designed to reduce the mean squared error in the presence of multicollinearity. The proposed method incorporates a preliminary estimator and a structured penalty term, yielding a closed-form solution that improves stability while preserving interpretability. Building on this estimator, a semi-parametric regression framework is developed by combining the new parametric model with support vector regression (SVR) to capture residual nonlinear patterns. The resulting two-stage approach effectively integrates linear structure and nonlinear flexibility. The proposed models are evaluated using simulated data and the concrete compressive strength dataset. Experimental results demonstrate that the semi-parametric approach substantially outperforms purely parametric methods
in terms of prediction accuracy, highlighting the effectiveness of the proposed penalization strategy and its integration with
SVR.
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