The New Estimation of Bi-response Nonparametric Regression Curve with Combined Estimators

To date, nonparametric regression studies using a combined estimator model have recently begun to develop significantly. Yet previous research employing this approach is still restricted to models with a single response variable. Hence, this paper offers a novel method to estimate bi-response nonparametric regression using a model that combines Fourier series and truncated spline estimators. This research aims to estimate the regression curve of the proposed model using two-stage estimation. The first stage is completed by the penalized weighted least square optimization followed by utilized the weighted least square optimization. We conduct numerical simulations with various sample sizes and correlations to assess the performance of the proposed model. Using generalized cross-validation as a criterion, the best model was obtained from the scenario model with big sample size and strong correlation. Furthermore, compared to uncombined estimators, the proposed model outperformed when applied to a real dataset of the human development index (HDI) education indicator in the East Java Province, Indonesia.