Estimation of Nonparametric Path Fourier Series and Truncated Spline Ensemble Models

To ascertain whether there is a causal connection between exogenous and endogenous factors, one method is to perform path analysis. The linearity assumption is the one that has the power to alter the model. The model's shape is impacted by the linearity assumption. The path analysis is parametric if the linearity assumption is true, but non-parametric path analysis is used if the non-linear form is unknown and there is no knowledge of the data pattern. If the non-linear form is unknown and there is no knowledge of the data pattern, non-linear path analysis is used. This study's goal was to calculate the nonparametric route function using a combination of truncated spline and Fourier series methods. The findings demonstrated that nonparametric path analysis only in cases where the linearity presumption is violated can one employ the Fourier series and truncated spline. Then, using the Ordinary Least Square (OLS) approach, the estimator of Nonparametric Regression-Based Path Analysis was obtained, delivering an estimation result that is not unique because it makes use of a nonparametric approach. The contribution of this paper can be used as reference material, especially analysis in statistics. With this paper, it is hoped that it can be applied in various fields. Suggestions for further research can develop this research with other models.