Pemilihan Bandwidth Optimal pada Regresi Nonparametrik Kernel Menggunakan Metode Unbiased Risk (UBR)

Muchni Illahi Efendi (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Jl. Raya ITS, Sukolilo, Surabaya, Indonesia 60111)
I Nyoman Budiantara (Departemen Statistika, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia)
Vita Ratnasari (Departemen Statistika, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia)

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

Nonparametric regression is used when the relationship pattern between the response and predictor variables is not clearly defined. Among several nonparametric regression approaches, the kernel method is commonly used. The selection of the optimal bandwidth is a key factor in kernel regression since it significantly affects the estimation accuracy. The optimal bandwidth selection can be obtained using the Unbiased Risk (UBR) method. The study aims to derive the mathematical formulation of the UBR method and evaluate its effectiveness in determining the optimal bandwidth for Indonesia’s 2024 economic growth rate data. The results indicate that the UBR method can be utilized in choosing the optimal bandwidth in nonparametric kernel regression for the economic growth rate data in Indonesia in 2024, producing bandwidths for each predictor of , and , with a minimum UBR of 2.827 and an MSE of 2.198. This implies that the nonparametric regression model with the optimal bandwidth obtained using the UBR method has good predictive capability with a relatively low estimation error for the economic growth rate data in Indonesia.