The nonparametric regression model using Fourier series approximation and penalized least squares (PLS) (case on data proverty in East Java)

Abstract

Poverty is a problem all countries in the world, particularly developing countries, should encounter. The poverty level of a country can be a benchmark to see its social and economic conditions. Java is an island with the highest poor population density in Indonesia with the level of population density of 14.83 million people. East Java province had percentage of poverty of 11.85% in 2016 and it was included in hard core poverty (above 10%), indicating that East Java was on the highest level of poverty. Therefore, regression model is required to find out factors significantly influencing poverty. The regression model used is nonparametric regression model since the scatter plot does not form certain plot and even tend to have repeated patterns of data on certain time interval. For that reason, Fourier series approximation is needed in nonparametric regression. On such approximation, the model parameter can be estimated based on penalized least squares (PLS) and minimum generalized cross validation (GCV). The study investigated and applied the regression model on data of poverty in East Java. The study resulted in parameter estimation of 18 parameters and values of λ of nonparametric regression of Fourier series ranging from 0.05 to 0.1 on M=1 and GCV value of 5.83028 with coefficient of determination (R2) of 83.28.