Kernel-Truncated Spline: Estimator Fleksibel untuk Regresi Nonparametrik

This study aims to develop a multivariable nonparametric regression model using a hybrid approach that combines Spline and kernel estimators. This method is proposed to address the limitations of conventional nonparametric models that typically apply a single type of estimator across all predictor variables, regardless of their individual patterns. In this approach, predictors with oscillatory patterns are modeled using truncated Spline regression, while variables exhibiting complex nonlinear behavior are modeled using a Gaussian kernel estimator. The combined model is constructed and estimated using the Ordinary Least Square (OLS) method and applied to data on the average years of schooling in South Sulawesi Province, Indonesia. Results indicate that the model using two Spline knots and an optimal bandwidth for the kernel component yields the lowest Generalized Cross Validation (GCV) value of 0.142, outperforming models with one or three knots. The best-fitting model achieves a coefficient of determination (R²) of 91.214% and a Mean Squared Error (MSE) of 0.0461. These findings suggest that the hybrid regression approach offers greater flexibility and accuracy in modeling multivariable social data.