Comparison of Nadaraya-Watson Method with Local Polynomial in Modeling Human Development Index and Poverty Relationship in Java

Abstract

Poverty remains a critical issue in Indonesia, with the number of poor people reaching 24.06 million in September 2024. The Human Development Index (HDI), which indicates the level of human resource quality, is one of the factors influence poverty. This analysis focuses on the correlation involving HDI also this number of poor people in districts/cities in Java Island by comparing two kernel regresokesion methods, namely Nadaraya-Watson Estimator and Local Polynomial Estimator. Nonparametric regression was chosen thus it does not necessitate this presumption of a certain form of connection among variables, so it is more flexible in capturing complex relationship patterns. Secondary data from Statistics Indonesia (BPS) in 2024 was used in this study. Initial exploration shows, the data distribution does not have a clear pattern, so nonparametric methods are more suitable for use. Modeling is done using the optimal bandwidth obtained through the dpill function in R software. The analysis results show that the local polynomial estimator produces smoother regression curves and lower MSE values. In addition, comparison of different polynomial degrees shows that higher polynomial degrees tended to improve model performance. Among the tested polynomial degrees, the local polynomial with degree five (p=5) produced the lowest MSE value and the highest coefficient of determination. Therefore, the local polynomial estimator with degree 5 is the best method for modeling the relationship between the HDI and poverty levels in Java in 2024