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%.

A method for parameter hypothesis testing in nonparametric regression with Fourier series approach

“…In nonparametric regression model with the Fourier series approach, parameter hypothesis testing has not been carried out previously. Referring to previous researches, this model was used by several researchers for modelling or even for prediction in various fields/data [see, 12 , [15] , [16] , [17] ]. However, these researches were only focused on estimation and modelling.…”

“…However, if the regression curve of is assumed to be only an unknown function and presented as a linear model as of (7) , then we could use the Ordinary Least Square (OLS) method that minimizes the sum of the square of the error. By using the optimization of the OLS method, the parameter estimation of could be obtained as follows [ 12 , [15] , [16] , [17] ]. where …”

Modeling Open Unemployment Rate in Kalimantan Island Using Nonparametric Regression With Fourier Series Estimator

“…One of the most popular estimation methods used by researchers is the Fourier series estimator [17]. The Fourier series is a trigonometric polynomial that has flexibility, so that it can adapt effectively to the local nature of the data [18], [19]. The Fourier series is generally used when the data pattern being investigated is unknown, and there is a tendency for the pattern to repeat [20], [21].…”

Fourier Series Application for Modeling “Chocolate” Keyword Search Trends in Google Trends Data

“…The Fourier series was introduced by Bilodeau (1992) as a form of trigonometry polynomial which has such flexibility that it can adjust and estimate the regression curve effectively [1], [2]. The Fourier Series tends to give good estimation results when applied to a regression curve with a repeating pattern [3]- [5].…”

“…Several studies that examine and develop the Fourier series approach include Dani and Adrianingsih (2020) regarding Nonparametric Regression Modeling with Truncated Spline Estimators and Fourier Series [3]. Octavanny et al (2021) modeled children ever born in Indonesia using Fourier series nonparametric regression [5]. Furthermore, Dani et al (2022) reviewed simulation studies and applications of the Fourier Series estimator in nonparametric regression modeling [19].…”