Mixture Model Nonparametric Regression and Its Application

Abstract

Regression analysis is a statistical analysis used to determine the pattern of relationships between predictor variables and response variables. There are two models of estimation approaches in regression analysis, namely parametric regression, and nonparametric regression. The parametric regression approach is used in the shape of the regression curve is known. In cases with unknown relationship patterns, the development is done using nonparametric regression. Nonparametric regression is a model estimation method which is based on an approach that is not bound by certain assumptions of the regression curve shape. Nonparametric regression varies greatly with variable curves that are different between one predictor variable with another predictor variable. In nonparametric regression, there are several types of the recommended kernel, spline, and Fourier series. In many cases, however, these conservative nonparametric regression methods cannot handle more complex problems. Mixture methods by combining several methods such as a mixture of spline and Fourier series, kernel and Fourier series, and so on, give a better result. This study aims to obtain estimates of a mixture of a truncated spline, kernel, and Fourier series by using the Ordinary Least Square (OLS) method and obtain methods for selecting knots, bandwidth, and optimal oscillation parameters with the smallest GCV. The results of this study are the formulation of a mixed estimation model of the truncated spline, kernel, and Fourier series and the smallest GCV formula to obtain the optimum location and number of points of knots, bandwidth, and oscillations.