Nonparametric regression estimator of multivariable Fourier Series for categorical data

In recent years, Fourier Series estimators in nonparametric regression for quantitative data have received significant attention. However, in reality, there is often a relationship between response and predictor, where the response is categorical data. Some methods developed today to address the case of qualitative response data use only certain approaches. No Fourier Series estimator can handle categorical response data. This paper introduces a new method that uses response variable in the form of categorical data. This study aimed to develop a multivariable Fourier Series nonparametric regression estimator for categorical data. The research methods used are literature and theoretical studies. To apply this method, we used two application data. The results obtained indicate that the nonparametric regression of the Fourier Series provides significantly better estimation results and accuracy for both data applications, due to the small deviance value and larger AUC and Press'Q values. The highlights of this research are summarized below.•The Fourier Series method for categorical data assumes a relationship between the logit function and predictor variables that has a repeating pattern.•The estimator was obtained through Maximum Likelihood Estimation and Newton-Raphson method.•The Fourier Series nonparametric regression method provides better estimation than binary logistic regression.