Interval estimation of semiparametric regression parameters fourier series

Regression is a statistical method that is used to explain the relationship between response variables and predictor variables. When the shape of regression curve consists of a known pattern of parametric component and an unknown pattern of nonparametric component, then the semiparametric regression can be considered as an alternative. When the patterns are not known and there is a tendency for patterns to repeat, the Fourier series estimator is frequently used. One of the main issues in statistical inference of regression is interval estimation (confidence interval). Many studies have been conducted on Fourier Series in Semiparametric Regression (FSSR), but most of these studies only address the method of generating the model estimators. There has been limited research on statistical inference aspects such as hypothesis testing and confidence interval for model parameters. The aim of this research is to obtain the interval estimation for the FSSR parameters model. The construction of interval estimation is done by Pivotal Quantity method. This study has found that the Pivotal Quantity follows student-t distribution. Using the Lagrange method for optimization, the shortest interval estimation for parameters of the FSSR model was obtained.