Fourier series estimator in semiparametric regression to predict criminal rate in Indonesia

Abstract

Regression is an analysis for determining relationship between response variables and predictor variables. There are three approaches to estimate the regression curve. Those are parametric regression, nonparametric regression, and semiparametric regression. This study focused on the estimator form of semiparametric regression curve using Fourier series approach with sine and cosine base (general); sine base; and cosine base. The best estimator, which is obtained using ordinary least square optimization was applied to model the percentage of criminal incidents in Indonesia. The goodness-of-fit criteria of a model used are high coefficient of determination, minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE) value with determining parsimony model. In this study, the authors obtained the best fourier estimator for predicting percentage of criminal incidents based on cosine fourier series that had minimun GCV and MSE values, of 2.471 and of 0.0006, respectively, and determination coefficient of 77.545%. So, the estimator (cosine-fourier series) was used for predicting the out-sample data and it met Mean Absolute Error (MAE) of 0.02.