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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. [ABSTRACT FROM AUTHOR]

In regression analysis, not all pattern of regression curve is known due to absence of prior information about the kind of relationship between response and predictor variable. In this case, nonparametric regression becomes an alternative solution since there is no assumption about parametric form. There are several functions in nonparametric regression one of which is truncated spline that is more flexible to fit the data, good at visual interpretation, and able to handle data that have changed behavior at certain subintervals. Moreover, some application involves more than one response variables that are correlated between responses. Therefore, this study aims to obtain the curve estimation of truncated spline estimators on bi-response nonparametric regression along with estimation of error variance-covariance matrix. The curve estimation of the truncated spline estimator was obtained by Weighted Least Square (WLS) optimization with Generalized Cross Validation (GCV) as optimal knot point selection method. Then, the curve estimation of the model was applied to a real dataset of the 2019 Human Development Index (HDI) and Gender Development Index (GDI) in East Java Province, Indonesia. HDI and GDI become indicators of Sustainable Development Goals (SDGs) achievement, particularly social and economic pillars. An adequate coefficient determination from the best model indicates that the model provides good performance in modeling the data. [ABSTRACT FROM AUTHOR]