Pemilihan Parameter Osilasi Optimal Menggunakan Generalized Cross-Validation (GCV) pada Regresi Nonparametrik Deret Fourier

Hasna Faridah Dhiya Ul Haq (Departemen Statistika, Fakultas Sains dan Matematika, Undip)
I Nyoman Budiantara (Departemen Statistika, Institut Teknologi Sepuluh Nopember, Jl. Teknik Mesin No 175, Keputih, Surabaya, Indonesia)
Jerry Dwi Trijoyo Purnomo (Departemen Statistika, Institut Teknologi Sepuluh Nopember, Jl. Teknik Mesin No 175, Keputih, Surabaya, Indonesia)

Jurnal Gaussian
Vol 14, No 2 (2025): Jurnal Gaussian

This research focuses on determining the optimal oscillation parameter in a Fourier series nonparametric regression model using the Generalized Cross-Validation (GCV) method to analyze factors influencing poverty in Central Java Province in 2024. The response variable is the percentage of the poor population, with Gross Regional Domestic Product (GRDP), Average Length of Schooling (ALS), and Open Unemployment Rate (OUR) as predictor variables. The optimal model is selected based on the minimum GCV value, with performance evaluated using MSE and . The results show that the minimum GCV is achieved at one oscillation, yielding an MSE of 4.545 and an  of 0.546, indicating that 54.6% poverty variation is explained by the predictors. Simultaneous testing shows a significant joint effect of predictors, while partial testing indicates no individual significance. Thus, GCV effectively determines the optimal oscillation parameter in Fourier series nonparametric regression for poverty analysis.