Mixture Model of Spline Truncated, Kernel, and Fourier Series in Semiparametric Regression
Ardiana Fatma Dewi (a), I Nyoman Budiantara (a*), Vita Ratnasari (a)

(a) Department of Statistics, Faculty of Science and Analytical Data, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia

Abstract

Regression analysis is one of the statistical methods used to investigate the relationship between the response variable and the predictor variable. In modeling, if several predictor variables affect the response variable, then there are the possibility of a combination of parametric and nonparametric patterns. It takes modeling that can accumulate the two combined patterns, a semiparametric regression approach. When the relationship between predictors variable and the response that follows a changing pattern at certain sub-intervals can be approached with a Spline Truncated estimator. If it does not follow a certain pattern it will be approached with Kernel estimator, whereas if it follows a recurring pattern and has a trend it will be approached with Fourier series estimator. Based on these problems, modeling can be done with an additive mixed estimator, where each predictor variable in the regression model is approached with an estimator that matches the curve shape of the response variable using the Ordinary Least Square (OLS) estimation method. Previous research has done modeling only one estimator and two estimators. So this study aims to perform modeling using a three-mixture estimator of Spline Truncated, Kernel, and Fourier Series in semiparametric regression. With this mixed estimator, it is expected that an estimate that is suitable for complex modeling will be generated with an estimate of the resulting R2 is higher.

Keywords: Fourier Series, Kernel, Semiparametric Regression, Spline Truncated

Topic: Mathematics Education