Mixture Estimators of Spline Truncated, Kernel, and Fourier Series in Biresponse Nonparametric Regression
Patrica Pungky Gabrela (a), Jerry Dwi Trijoyo Purnomo (b*), I Nyoman Budiantara (b)

a) Master Program of Statistics Departement, Sepuluh Nopember Institute of Technology, Sukolilo, Surabaya, Indonesia
b) Statistics Departement, Sepuluh Nopember Institute of Technology, Sukolilo, Surabaya, Indonesia
*jerry[at]statistika.its.ac.id

Abstract

The general regression model is divided into three forms, namely parametric, nonparametric, and semiparametric model. Regression is a method used to analyze the relationship between response variables and predictor variables. The shape of the regression model depends on the regression curve. Nonparametric regression has become a concern of many researchers because it can determine the relationship between the predictor variable and the response variable which has an unknown regression curve. Nonparametric regression is very flexible so that the model can follow linear or nonlinear functions. Several nonparametric regression approaches that are often used are Spline Truncated, Kernel, and Fourier Series. Until now, many studies related to nonparametric regression have been carried out, either with a single estimator or a mixed estimator. So far, research with mixed estimators mostly uses only two estimators. There have not been many studies related to nonparametric regression models involving 3 mixed estimators. Therefore, the purpose of this study is to find a mixture estimator of Spline Truncated, Kernel, and Fourier Series in the biresponse nonparametric regression using the WLS method. The results show that the WLS estimation produces a Spline Truncated estimator, Kernel estimator, Fourier Series estimator, and also a mixture of the 3 estimators.

Keywords: Biresponse Nonparametric Regression- Fourier Series- Kernel- Spline Truncated

Topic: Mathematics