Search

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 twostage 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. [ABSTRACT FROM AUTHOR]

Nonparametric regression becomes a potential solution if the parametric regression assumption is too restrictive while the regression curve is assumed to be known. In multivariable nonparametric regression, the pattern of each predictor variable's relationship with the response variable is not always the same; thus, a combined estimator is recommended. In addition, regression modeling sometimes involves more than one response, i.e., multiresponse situations. Therefore, we propose a new estimation method of performing multiresponse nonparametric regression with a combined estimator. The objective is to estimate the regression curve using combined truncated spline and Fourier series estimators for multiresponse nonparametric regression. The regression curve estimation of the proposed model is obtained via two-stage estimation: (1) penalized weighted least square and (2) weighted least square. Simulation data with sample size variation and different error variance were applied, where the best model satisfied the result through a large sample with small variance. Additionally, the application of the regression curve estimation to a real dataset of human development index indicators in East Java Province, Indonesia, showed that the proposed model had better performance than uncombined estimators. Moreover, an adequate coefficient of determination of the best model indicated that the proposed model successfully explained the data variation. [ABSTRACT FROM AUTHOR]