A method for parameter hypothesis testing in nonparametric regression with Fourier series approach

Abstract

Nonparametric regression model with the Fourier series approach was first introduced by Bilodeau in 1994. In the later years, several researchers developed a nonparametric regression model with the Fourier series approach. However, these researches are limited to parameter estimation and there is no research related to parameter hypothesis testing. Parameter hypothesis testing is a statistical method used to test the significance of the parameters. In nonparametric regression model with the Fourier series approach, parameter hypothesis testing is used to determine whether the estimated parameters have significance influence on the model or not. Therefore, the purpose of this research is for parameter hypothesis testing in the nonparametric regression model with the Fourier series approach. The method that we use for hypothesis testing is the LRT method. The LRT method is a method that compares the likelihood functions under the parameter space of the null hypothesis and the hypothesis. By using the LRT method, we obtain the form of the statistical test and its distribution as well as the rejection region of the null hypothesis. To apply the method, we use ROA data from 47 go public banks that are listed on the Indonesia stock exchange in 2020. The highlights of this research are:•The Fourier series function is assumed as a non-smooth function.•The form of the statistical test is obtained using the LRT method and is distributed as F distribution.•The estimated parameters on modelling ROA data have a significant influence on the model.