The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression

Abstract

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.