A New Nonparametric Regression Approach Using a Three-Mixed Estimator (T-MENR) with Application in Public Health Data: A Case Study of Prevalence of Hypertension

Abstract

This study proposes a novel Three-Mixed Estimator Nonparametric Regression (T-MENR) model to address the limitations of conventional single and two-mixed estimator approaches in capturing complex nonlinear relationships. The proposed framework integrates truncated spline, Gaussian kernel, and Fourier series estimators within a unified additive structure, allowing each predictor variable to be modeled according to its underlying pattern. The optimal model configuration is determined using the Generalized Cross-Validation (GCV) criterion by evaluating 54 possible estimator combinations. The empirical application to hypertension prevalence data in Indonesia shows that the best model (C27) achieves strong performance, with a minimum GCV value of 0.1972, RMSE of 0.4902, and coefficient of determination (R2) of approximately 0.9536. These results indicate that the T-MENR model is highly effective in explaining variability in hypertension prevalence. Compared to single nonparametric models, the proposed approach consistently produces lower prediction error and higher explanatory power, demonstrating the advantage of combining multiple estimators within a single framework. The results also reveal that different health behavioral factors follow distinct relationship patterns, which are better represented when modeled using appropriate estimators. Despite its strong performance, the model requires substantial computational effort due to the large number of parameter combinations. Future research may focus on incorporating statistical inference, such as hypothesis testing, to further improve model interpretability.