Optimal Knots Point and Bandwidth Selection in Modeling Mixed Estimator Nonparametric Regression

Abstract

The nonparametric regression model that is currently developing is limited to only one estimator form that is used. This happens, due to the assumption from the researcher that each of these predictors has the same data pattern. However, when we model the predictor variable with the response variable, what happens is that each predictor may have a different pattern, so it is necessary to develop a mixed estimator. The mixed estimator used in this study is the truncated spline and the Gaussian Kernel. Furthermore, it becomes a separate problem, when combining the truncated spline with the Gaussian Kernel, so it must determine the optimal knot point and bandwidth. Determine the optimal knot point and bandwidth is very important. The methods used are Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). In this study, the nonparametric regression model was applied to the data on the percentage of poor people in Districts/Cities on Borneo Island in 2019. Based on analysis, the modeling of the nonparametric regression approach with a mixed estimator of the truncated spline and the Gaussian Kernel uses the GCV method which gives the best results. This is supported by the coefficient of determination obtained by 90.52% and the MSE value of 1.10. This means that the nonparametric regression model built can explain the effect of the predictor variable on the response variable, namely the percentage of poor people by 90.52%.