A reproducing kernel hilbert space approach and smoothing parameters selection in spline-kernel regression

Regression analysis studies the form of the relationship between one or more predictor variables with one response variable. The relationship of the response variable with several predictor variables in nonparametric regression does not always using one type of approach such as Spline, Kernel, or Fourier series. This fact is found in many nonparametric regression, between one predictor variable and another predictor variable that has a different pattern with the response variable. This study proposes a model that has ability to handle the different patterns in the nonparametric regression. This model was developed by adding Kernel functions to the goodness of fit component in completion of the smoothing Spline. Empirical analysis is carried out on fuel consumption data in Indonesia. The performance of the proposed model is evaluated by looking at the GCV value and comparing its coefficient of determination with the parametric regression. The result of the study shows that the proposed model is better than the compared model. In addition, this model has a highly accuracy in making predictions or forecasting.