COMPARISON OF GENERALIZED CROSS VALIDATION (GCV) METHODS WITH CROSS VALIDATION (CV) TO DETERMINE OPTIMAL KNOTS IN FOURIER SERIES NONPARAMETRIC REGRESSION (Case Study: Poverty Rate in North Sumatra Province)

Abstract

Poverty is multidimension problem that directly affected human life. North Sumatera Province is a province with the most poor population in Sumatera Island that is 1453.87 (thousand souls). A factor thought to affect the high poverty rate in the northern province of sumatera is per capita income. Distribution of data on the number of poor people and per capita income of each regency/city in North Sumatera Province tends to be repetitive and the pattern is unknown, then in this study used a nonparametric regression approach of fourier series. The purpose of this study is to model poverty in regency/city in North Sumatera Province using nonparametric regression fourier series with GCV and CV methods to determine the optimal knots (K) and compare the results of modelling based on GCV and CV methods to determine the optimal K in nonparametric regression with fourier series. The population in this study were all regency/cities in North Sumatera Province, amounting to 33 regency/cities. The results showed that the GCV method in determining the optimal K in the nonparametric regression of the fourier series was better than the CV method for modelling poverty levels in North Sumatera Province. The GCV method produces an R² of 96% with an MSE value of 52.14 while the CV method produces an R² 67% with an MSE value of 463.62. The results of the analysis of poverty level modelling in North Sumatera Province in 2017 with the GCV method for determining optimal K in nonparametric regression of fourier series obtained the highest poverty estimate of 134.52 (thousand inhabitants) found in Medan City and the lowest poverty estimate of 11.05 (thousand inhabitants) found in Pakpak Bharat Regency.