Umami, Shinta Istibsyaroh (2025) Pemilihan Titik Knot dan Parameter Osilasi Optimal dengan Metode Cross-Validation (CV), Generalized Cross-Validation (GCV), dan Unibiased Risk (UBR) Pada Regresi Nonparametrik Estimator Campuran Spline Truncated dan Deret Fourier. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Pendekatan regresi nonparametrik digunakan ketika bentuk pola antar variabel respon dengan variabel prediktor tidak diketahui. Terdapat beberapa metode dalam regresi nonparametrik seperti spline truncated dan deret Fourier. Pada regresi nonparametrik spline truncated menentukan titik knot optimal menjadi hal yang sangat penting dan krusial, sama halnya pada regresi nonparametrik deret Fourier yang harus menentukan parameter osilasi. Penentuan titik knot dan parameter osilasi optimal dalam model regresi nonparametrik estimator campuran spline truncated dan deret Fourier akan sangat mempengaruhi kurva regresi yang akan terbentuk. Terdapat beberapa metode yang dapat digunakan dalam pemilihan titik knot dan parameter osilasi optimal, seperti metode Cross-Validation (CV), Generalized Cross-Validation (GCV), dan Unbiased Risk (UBR). Tujuan penelitian ini mengkaji metode CV, GCV, dan UBR untuk memilih titik knot dan parameter osilasi optimal dalam regresi nonparametrik estimator campuran spline truncated dan deret Fourier. Kemudian dilakukan perbandingan pemilihan titik knot dan parameter osilasi menggunakan metode CV, GCV, dan UBR yang diterapkan pada data Persentase Kemiskinan di Pulau Jawa tahun 2023. Metode estimasi yang digunakan adalah Ordinary Least Square (OLS). Hasil analisis mendapatkan nilai R2 metode CV dan GCV adalah sama yakni sebesar 61,934% sedangkan nilai R2 untuk metode UBR lebih kecil yakni sebesar 50,114%. Artinya, metode CV dan GCV merupakan metode terbaik untuk pemilihan titik knot dan parameter osilasi optimal pada regresi nonparameterik estimator campuran spline truncated dan deret Fourier dengan banyak titik knot optimal adalah dua dan parameter osilasi optimal adalah satu
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The nonparametric regression approach is used when the pattern shape between the response variable and the predictor variable is unknown. There are several methods in nonparametric regression such as truncated spline and Fourier series. In nonparametric truncated spline regression, determining the optimal knot point is very important and crucial, as well as in nonparametric Fourier series regression which must determine the oscillation parameters. Determining the optimal knot point and oscillation parameters in the nonparametric regression model of the mixed estimator of the truncated spline and Fourier series will greatly affect the regression curve that will be formed. There are several methods that can be used in selecting the optimal knot point and oscillation parameters, such as the Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) methods. The purpose of this study is to examine the CV, GCV, and UBR methods to select the optimal knot point and oscillation parameters in nonparametric regression of the mixed estimator of the truncated spline and Fourier series. Then a comparison of the selection of knot points and oscillation parameters using the CV, GCV, and UBR methods was applied to the Poverty Percentage data in Java Island in 2023. The estimation method used is Ordinary Least Square (OLS). The results of the analysis obtained the R2 value of the CV and GCV methods were the same, namely 61.934%, while the R2 value for the UBR method was smaller, namely 50.114%. This means that the CV and GCV methods are the best methods for selecting knot points and optimal oscillation parameters in nonparameteric regression of mixed estimators of truncated splines and Fourier series with the number of optimal knot points being two and the optimal oscillation parameter being one.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Cross-Validation, Deret Fourier, Generalized Cross-Validation, Regresi Nonparametrik, Spline Truncated, dan Unbiassed Risk Cross-Validation, Fourier series, Generalized Cross-Validation, Nonparametric Regression, Truncated Spline, and Unbiased Risk |
| Subjects: | 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: | Shinta Istibsyaroh Umami |
| Date Deposited: | 28 Jan 2025 22:49 |
| Last Modified: | 28 Jan 2025 22:49 |
| URI: | http://repository.its.ac.id/id/eprint/117053 |
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