The estimation of mixed truncated spline and Fourier series estimator in bi-response nonparametric regression

Due to the lack of prior knowledge regarding the type of relationship between the response and the predictor variable, not all patterns of the regression curve are identifiable in regression analysis. Hence, nonparametric regression becomes a reasonable solution since no prespecified functional form is assumed. In nonparametric regression, curve estimation using a mixed estimator is rather complex, notably when there are two or more correlated response variables. In this study, we developed the curve estimation of bi-response nonparametric regression with a mixed truncated spline and Fourier series estimator model. The main objective was to estimate the regression curve using penalized weighted least square and weighted least square optimization. Based on the estimation results, numerical simulations with various sample sizes and correlations were implemented with generalized cross validation as the criterion. Thus, the model with a large sample size and high correlation was performed with the best outcome.