Sukran, Ade Matao (2025) Pemodelan Regresi Nonparametik Multirespon dengan Estimator Campuran Spline Truncated, Deret Fourier, dan Kernel. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
kurang mampu menangkap variasi pola data yang kompleks antar variabel prediktor. Meskipun penelitian dengan estimator campuran telah ada, penerapannya masih terbatas pada model dengan satu atau dua respon. Penelitian ini bertujuan untuk mengkaji dan menerapkan model regresi nonparametrik multirespon dengan estimator campuran spline truncated, deret Fourier, dan kernel untuk memodelkan faktor-faktor yang memengaruhi indikator kemiskinan di Provinsi Jawa Timur. Metode ini diaplikasikan pada data sekunder BPS tahun 2024 untuk 38 kabupaten/kota di Jawa Timur, yang melibatkan tiga variabel respon (Persentase Penduduk Miskin, Indeks Kedalaman Kemiskinan, dan Indeks Keparahan Kemiskinan) dan empat variabel prediktor (Umur Harapan Hidup, Rata-rata Lama Sekolah, Pengeluaran Per Kapita, dan Tingkat Partisipasi Angkatan Kerja). Hasil penelitian menunjukkan model terbaik adalah kombinasi dua prediktor spline truncated (Umur Harapan Hidup & Rata-rata Lama Sekolah), satu prediktor deret Fourier (Pengeluaran per Kapita), dan satu prediktor kernel (Tingkat Partisipasi Angkatan Kerja). Model optimal ini, yang dipilih berdasarkan nilai Generalized Cross Validation (GCV) terkecil yaitu 1,863, menggunakan 2 titik knot dan 1 osilasi. Model ini mampu menjelaskan keragaman data Indikator Kemiskinan sebesar 95,883%, dengan nilai MSE sebesar 0,996. Disimpulkan bahwa pemodelan regresi nonparametrik multirespon dengan estimator campuran lebih baik dalam memodelkan Indikator Kemiskinan di Jawa Timur dibandingkan model dengan estimator tunggal.
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Nonparametric regression often uses a single estimator, making it less capable of capturing complex data pattern variations among predictor variables. Although studies using mixed estimators exist, their application has been limited to models with one or two responses. This study aims to examine and apply a multiresponse nonparametric regression model using a mixed estimator of spline truncated, Fourier series, and kernel to model the factors affecting poverty indicators in East Java Province. This method was applied to secondary data from BPS for 38 districts/cities in East Java for the year 2024, involving three response variables (Percentage of Poor Population, Poverty Depth Index, and Poverty Severity Index) and four predictor variables (Life Expectancy, Average Years of Schooling, Per Capita Expenditure, and Labor Force Participation Rate). The results show that the best model is a combination of two spline truncated predictor (Life Expectancy and Average Years of Schooling), one Fourier series predictor (Per Capita Expenditure), and one kernel predictors (Labor Force Participation Rate). This optimal model, selected based on the smallest Generalized Cross Validation (GCV) value of 1,863, utilizes 2 knots and 1 oscillation. This model can explain 95,883% of the variance in the Poverty Indicator data, with an MSE value of 0,996. It is concluded that the multiresponse nonparametric regression model with a mixed estimator is superior for modeling Poverty Indicators in East Java compared to models with a single estimator.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Deret Fourier, Kemiskinan, Kernel, Regresi Nonparametrik Multirespon, Spline Truncated, Fourier Series, Kernel, Multiresponse Nonparametric Regression, Poverty, Spline Truncated. |
| Subjects: | H Social Sciences > HA Statistics > HA31.3 Regression. Correlation. Logistic regression analysis. H Social Sciences > HA Statistics > HA31.7 Estimation Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA353.K47 Kernel functions (analysis) Q Science > QA Mathematics > QA404 Fourier series |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Ade Matao Sukran |
| Date Deposited: | 04 Aug 2025 09:09 |
| Last Modified: | 04 Aug 2025 09:09 |
| URI: | http://repository.its.ac.id/id/eprint/125096 |
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