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I Nyoman Budiantara
Departemen Statistika, Institut Teknologi Sepuluh Nopember, Jl. Teknik Mesin No 175, Keputih, Surabaya, Indonesia
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Pemilihan Parameter Osilasi Optimal Menggunakan Generalized Cross-Validation (GCV) pada Regresi Nonparametrik Deret Fourier Hasna Faridah Dhiya Ul Haq; I Nyoman Budiantara; Jerry Dwi Trijoyo Purnomo
Jurnal Gaussian Vol 14, No 2 (2025): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/j.gauss.14.2.577-587

Abstract

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.
Estimator Campuran Spline Truncated dan Deret Fourier dalam Regresi Nonparametrik Untuk Data Kategori Kadek Adi Surya Negara; I Nyoman Budiantara; Vita Ratnasari
Jurnal Gaussian Vol 14, No 2 (2025): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/j.gauss.14.2.588-598

Abstract

Nonparametric regression analysis is ideal when data patterns are uncertain because the approach is highly flexible. In some nonparametric cases, each predictor variable exhibits a different form of association with the response variable. Using only one estimator may result in estimates that do not align with the actual data patterns. Therefore, a mixed estimator approach is needed to overcome this problem. This research introduces a truncated spline and Fourier series mixed estimator, in which the relational structure between the response and predictor variables changes across certain intervals, while others demonstrate a recurring pattern. However, most studies on nonparametric regression still use response variables expressed as quantitative data, even though there are conditions where the response variables are categorical data. Therefore, this study will develop a mixed estimator for categorical data. This study aims to obtain truncated spline and Fourier series mixed estimators in nonparametric regression for categorical data using the Maximum Likelihood Estimation method followed by Newton Raphson iteration. This study produces parameter estimators in mixed models by combining truncated spline functions and Fourier series functions in binary categorical data using the Newton Raphson iteration approach.
Co-Authors Hasna Faridah Dhiya Ul Haq Jerry Dwi Trijoyo Purnomo Kadek Adi Surya Negara Vita Ratnasari