Statistical inferences and applications of nonparametric regression models based on fourier series

This study develops statistical inference methods, including estimation and hypothesis testing procedures, which consist of partial and simultaneous tests for nonparametric regression models based on Fourier series approximations. The Fourier series is effective for data with periodic characteristics, offering flexible nonparametric regression solutions. While previous work primarily focused on estimation techniques, this research introduces a structured hypothesis testing framework using F-test and T-test statistics to evaluate the significance of model parameters. Utilizing real-world expenditure data from 29 districts in Papua, Indonesia, we examine the Gross Regional Domestic Product per capita, poverty rates, and labor force participation rates as predictors of per capita expenditure. The best oscillation parameter is determined through Generalized Cross Validation (GCV), improving the accuracy of the model. The findings demonstrate significant effects of the predictor variables on the model, supported by both simultaneous tests using the F-test and partial tests using T-tests. The highlights of this research are:•Introduces hypothesis testing using F-test and T-test for nonparametric regression with Fourier series.•Applies model to regional expenditure data with optimal parameter selection.•Validates model using real data, showing significant predictor influence.