Wardani, Putri Kusuma (2023) Pemilihan Titik Knot dan Parameter Osilasi Optimal Menggunakan Metode Generalized Cross-Validation (GCV) dan Unbiased Risk (UBR) Pada Regresi Nonparametrik Estimator Campuran Spline Truncated Dan Deret Fourier. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Bentuk pola antar variabel respon dengan variabel prediktor yang tidak diketahui, maka pendekatan yang sesuai dengan kasus tersebut adalah pendekatan regresi nonparametrik. 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 Generalized Cross-Validation (GCV) dan Unbiased Risk (UBR). Tujuan pada penelitian ini untuk mengkaji metode 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 GCV dan UBR pada data yang digunakan pada penelitian ini yaitu data laju pertumbuhan ekonomi di Indonesia tahun 2022. Metode estimasi yang digunakan adalah Ordinary Least Square (OLS). Didapatkan nilai MSE metode GCV sebesar 1,42 dimana nilai tersebut lebih kecil dari nilai MSE metode UBR yaitu 10,614. Artinya, metode GCV merupakan metode terbaik untuk pemilihan titik knot dan parameter osilasi optimal pada regresi nonparametrik estimator campuran spline truncated dan deret Fourier dengan banyak titik knot optimal sebanyak tiga dan parameter osilasi optimal sebanyak tiga. Nilai koefisien determinasi metode GCV sebesar 89,34%.
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If the shape of the pattern between the response variables and the predictor variables is not known, then the approach that is suitable for this case is a nonparametric regression approach. There are several methods in nonparametric regression such as spline truncated and Fourier series. In spline truncated nonparametric regression determining the optimal knot point is very important and crucial, as is in Fourier series nonparametric regression which determines the oscillation parameters. Determination of the knot points and oscillation parameters in nonparametric regression of combined estimators spline truncated and Fourier series will affect the regression curve that will be formed. There are several methods that can be used in selecting optimal knot points and oscillation parameters, namely the Generalized Cross-Validation (GCV) and Unbiased Risk (UBR) methods. The aim of this study was to examine the GCV and UBR methods to select knot points and optimal oscillation parameters in nonparametric regression of combined estimators spline truncated and Fourier series. Then a comparison of the selection of knot points and oscillation parameters using the GCV and UBR methods on the data on the rate of economic growth Indonesia in 2022. The estimation method used is Ordinary Least Square (OLS). The MSE value for the GCV method was 1,42 which is smaller than the MSE value for the UBR method, which was 10,614. Tat mean the GCV method is the best method for selecting optimal knot points and oscillation parameters in nonparametric regression of combined estimators spline truncated and Fourier series with three optimal knot points and three optimal oscillation parameters. The coefficient of determination GCV method of 89,34%.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Deret Fourier, Generalized Cross-Validation, Regresi Nonparametrik, Spline Truncated, dan Unbiassed Risk, Fourier series, Generalized Cross-Validation, Nonparametric Regression, Truncated Spline, and Unbiased Risk. |
| Subjects: | H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HA Statistics > HA31.3 Regression. Correlation H Social Sciences > HA Statistics > HA31.7 Estimation Q Science Q Science > QA Mathematics > QA404 Fourier series |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Putri Kusuma Wardani |
| Date Deposited: | 08 Aug 2023 06:40 |
| Last Modified: | 08 Aug 2023 06:40 |
| URI: | http://repository.its.ac.id/id/eprint/104283 |
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