Parameter estimation of spline truncated, kernel, and Fourier series mixed estimators in semiparametric regression

Abstract

Regression is a statistical analysis method used to investigate the relationship between response and predictor variables. Along with the development of increasingly complex problems, forcing researchers to involve several predictor variables. So that it is possible to have a combination of parametric and nonparametric patterns, for this reason, modeling is needed to accumulate the two combined patterns with a semiparametric regression approach. When the relationship between predictor and response variables follows a changing pattern at a certain subinterval, it can be approximated by the Spline Truncated estimator, if it does not follow a certain pattern, it can be approached with the Kernel estimator. On the other hand, if it follows the tendency of a repeating pattern, it is approximated by a Fourier Series estimator. Spline, Kernel, and Fourier Series truncated estimators are often used because they have several advantages and are more flexible. Based on these problems, modeling can be done with an additive mixture estimator, where each predictor variable in the regression model is approached with an estimator that matches the shape of the response variable curve using the Ordinary Least Square (OLS) estimation method. In recent years, many researchers have done modeling with only one or two estimators. So that in this study the aim is to develop theory with three mixed estimators, namely Spline Truncated, Kernel, and Fourier Series in semiparametric regression. One application can be used to model data related to social and population which has a tendency of different relationship patterns on each predictor variable of response. With this mixed estimator, the resulting error is smaller so that it will produce a minimum GCV value.