Estimator Ridge-deret Fourier Pada Regresi Nonparametrik

Muthahharah, Sidratul (2026) Estimator Ridge-deret Fourier Pada Regresi Nonparametrik. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Regresi nonparametrik banyak digunakan untuk memodelkan hubungan antara variabel ketika bentuk fungsi regresi tidak diketahui pasti. Estimator deret Fourier efektif dalam menangkap pola berulang. Namun, pada kasus multivariabel, korelasi yang kuat antar variabel prediktor dapat menyebabkan multikolinearitas yang mengakibatkan estimasi parameter menjadi tidak stabil akibat matriks desain yang mendekati singular. Meskipun estimator berbasis deret Fourier telah banyak dikembangkan, formulasinya belum secara eksplisit mengatasi permasalahan tersebut. Penelitian ini mengusulkan estimator ridge–deret Fourier dalam regresi nonparametrik untuk memperoleh estimasi parameter yang stabil pada kondisi multikolinearitas. Estimator diturunkan dalam tahapan likelihood terpinalti dengan mengintegrasikan penalti ridge ke dalam model deret Fourier. Parameter osilasi dan penalti ridge dipilih menggunakan kriteria Generalized Cross Validation (GCV).
Metode yang diusulkan diterapkan pada data Tingkat Pengangguran Terbuka tahun 2024 pada kabupaten/kota di Jawa Barat. Model teroptimal diperoleh pada kombinasi osilasi [4, 4, 4, 2] dengan parameter ridge sebesar 0,034904 dan koefisien determinasi sebesar 91,08%, menunjukkan bahwa estimator ridge–deret Fourier yang diusulkan mampu memberikan estimasi parameter yang stabil serta meningkatkan kinerja prediksi pada kondisi multikolinearitas.
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Nonparametric regression is widely used to model relationships between variables when the functional form of the regression curve remains unspecified. The Fourier series estimator is effective for capturing periodic patterns. However, in multivariable settings, strong correlations among predictors may lead to multicollinearity, resulting in unstable parameter estimates due to the nearsingularity of the design matrix. Although Fourier-based estimators have been extensively developed, their formulation has not explicitly addressed this issue. This study proposes a ridge-Fourier series estimator for nonparametric regression to obtain stable parameter estimation in the presence of multicollinearity. The estimator is derived within a penalized likelihood framework by incorporating a ridge penalty into the Fourier series representation and estimating the parameters. The oscillation and ridge penalty parameters are selected using the Generalized Cross Validation (GCV) criterion.
The proposed method is applied to the 2024 Open Unemployment Rate data covering districts and cities in West Java. The optimal model is obtained at the oscillation combination of [4, 4, 4, 2] with a ridge parameter of 0,034904, accompanied by a coefficient determination of 91.08%, indicating that the proposed ridge-Fourier Series estimator provides more stable estimation and improved predictive performance under multicollinearity conditions.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Multikolinearitas, Regresi Nonparametrik Deret Fourier, Regresi Ridge, Tingkat Pengangguran terbuka (TPT). ========================================================== Multicollinearity, Nonparametric Fourier Series Regression, Ridge Regression, Open Unemployment Rate (TPT).
Subjects:	H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HA Statistics > HA31.3 Regression. Correlation. Logistic regression analysis. H Social Sciences > HA Statistics > HA31.7 Estimation
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Sidratul Muthahharah
Date Deposited:	21 Jul 2026 03:21
Last Modified:	21 Jul 2026 03:21
URI:	http://repository.its.ac.id/id/eprint/135877

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