Modeling of Children Ever Born in Indonesia Using Fourier Series Nonparametric Regression

Abstract

Nonparametric regression aims to determine the relationship between response and predictor when the data does not follow a specific pattern. Fourier series is a nonparametric regression approach which has the flexibility to follow the characteristics of data. The purpose of this study is to obtain the estimator of the nonparametric regression using Fourier series and apply the model to the fertility data. The fertility rate represented by children ever born is one of the demographic factors that determine the decline in population growth rate. The data were obtained from the Indonesia Demographic and Health Survey 2017 with children ever born as a response. The predictors are the proportion of women graduating from junior high school, the proportion of women having sex before the age of 18, the proportion of women using a modern contraceptive method, and the infant mortality rate. The relationship between response and predictors tends to have a repetitive pattern with a certain trend. The best nonparametric regression model of children ever born in Indonesia is obtained by using 3 oscillation parameters for each predictor variable with GCV = 0.0534 and R-square = 80.04%.