Regresi Nonparametrik Kernel Triangle dan Gaussian dengan Estimator Priestley-Chao untuk Pemodelan Kasus AIDS di Pulau Jawa

Abstract

Infection with the Human Immunodeficiency Virus (HIV). In Indonesia, the number of AIDS cases increased in 2023, with the highest cases recorded in provinces on the island of Java. This study aims to model the relationship between socioeconomic factors and the number of AIDS cases in Java using the Priestley-Chao kernel nonparametric regression. The nonparametric approach was chosen for its flexibility and because it does not require assumptions about the form of the relationship. The Priestley-Chao estimator has the advantage of producing smooth estimates even with limited data. This study compares two kernel functions: the triangle kernel, which performs well in modeling fluctuating data, and the Gaussian kernel, which is defined over all real numbers. The analysis showed that the best triangle kernel model was obtained with a bandwidth combination of h1 = 0.10, h2 = 0.20, and h3 = 0.25, resulting in a minimum GCV value of 0.003178. The best Gaussian kernel model was found at h1 = 0.10, h2 = 0.14, and h3 = 0.10, with a minimum GCV value of 0.008402. Based on MSE and R² values, the triangle kernel demonstrated better performance (MSE = 0.003129; R² = 0.887730) compared to the Gaussian kernel (MSE = 0.008247; R² = 0.704080).