Pemilihan Titik Knot dan Parameter Osilasi Optimal Menggunakan Metode GCV dan UBR pada Regresi Semiparametrik Estimator Campuran Spline Truncated dan Deret Fourier

Habibah, Askin Nur (2025) Pemilihan Titik Knot dan Parameter Osilasi Optimal Menggunakan Metode GCV dan UBR pada Regresi Semiparametrik Estimator Campuran Spline Truncated dan Deret Fourier. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Regresi semiparametrik adalah pendekatan regresi yang menggabungkan komponen parametrik dan nonparametrik. Terdapat beberapa metode dalam regresi semiparametrik diantaranya adalah spline truncated dan deret Fourier. Penentuan titik knot pada Spline truncated dan parameter osilasi pada deret Fourier memiliki peran yang sangat penting dalam meningkatkan akurasi model serta mempengaruhi bentuk kurva regresi yang dihasilkan. Dalam hal ini, metode Generalized Cross-Validation (GCV) dan Unbiased Risk (UBR) adalah dua pendekatan yang sering digunakan dalam pemilihan titik knot dan parameter osilasi optimal. Tujuan pada penelitian ini untuk mengkaji metode GCV dan UBR dalam menentukan titik knot dan parameter osilasi yang optimal dalam regresi semiparametrik estimator campuran Spline truncated dan deret Fourier. Selanjutnya, dilakukan perbandingan metode GCV dan UBR pada data produksi beras tahun 2023. Metode estimasi yang digunakan adalah Ordinary Least Least Square (OLS). Hasil simulasi menunjukkan bahwa performa metode bergantung pada ukuran sampel, distribusi error, dan variansnya. Pada error berdistribusi normal, metode GCV lebih stabil, baik pada varians rendah (
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Semiparametric regression is regression approach that combines parametric and nonparametric components. There are several methods in semiparametric regression including spline truncated and Fourier series. Determination of knot points in Truncated Spline and oscillation parameters on the Fourier series has a very important role in improve the accuracy of the model and affect the shape of the resulting regression curve. In this case, the Generalized Cross-Validation (GCV) and Unbiased Risk (UBR) methods are used. Unbiased Risk (UBR) are two approaches that are often used in the selection of optimal knot points and oscillation parameters. The purpose of this study to examine the GCV and UBR methods in determining the optimal knot points and oscillation parameters in semiparametric regression of mixed estimator of Spline and Fourier series. Furthermore, a comparison of the GCV and UBR methods on rice production data in 2023. The estimation method used is Ordinary Least Least Square (OLS). The simulation results show that the performance of the method depends on the sample size, error distribution, and variance. For normally distributed errors, the GCV method is more stable, both at low (

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Deret Fourier, Generalized Cross Validation, Regresi Semiparametrik, Spline truncated, Unbiased Risk. =========================================================== Fourier Series, Generalized Cross Validation, Semiparametric Regression, Spline truncated, Unbiased Risk
Subjects:	H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HA Statistics > HA31.7 Estimation Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA404 Fourier series
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Askin Nur Habibah
Date Deposited:	06 Feb 2025 06:07
Last Modified:	06 Feb 2025 06:07
URI:	http://repository.its.ac.id/id/eprint/118371

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