Ayuningtiyas, Nadiah Ulfa (2022) Perbandingan Pemilihan Titik Knot Optimal Dengan Cross Validation (CV), Generalized Cross Validation (GCV) Dan Unbiased Risk (UBR) Pada Regresi Nonparametrik Truncated Spline Birespon. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Regresi dikembangkan oleh para peneliti menjadi tiga jenis, yaitu regresi parametrik, regresi nonparametrik, dan regresi semiparametrik. Beberapa model regresi nonparametrik yang banyak digunakan antara lain spline, deret fourier, kernel, wavelets, dan lain sebagainya. Spline merupakan model yang mempunyai interpretasi statistik dan interpretasi visual yang sangat khusus dan sangat baik. Terdapat tiga kriteria dalam pembentukan model regresi spline, yaitu menentukan orde untuk model, banyakanya knot dan lokasi penempatan knot. Beberapa metode yang digunakan untuk memilih titik knot optimal dalam regresi nonparametrik spline, antara lain metode Cross Validation (CV), Generalized Cross Validation (GCV) dan Unbiassed Risk (UBR). Tujuan penelitian ini adalah untuk mengkaji pemilihan titik knot optimal dengan metode CV, GCV dan UBR pada model regresi nonparametrik spline truncated respon birespon. Studi kasus pada penelitian ini yaitu persentase penduduk miskin dan indeks keparahan kemiskinan Kabupaten/Kota di Provinsi Jawa Timur Tahun 2020. Berdasarkan hasil analisis, ditunjukkan bahwa metode GCV lebih baik dalam mendapatkan titik knot optimal dibandingkan metode CV dan UBR. Metode GCV menggunakan tiga titik knot optimal didapatkan nilai R2 sebesar 95,763%.
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Regression was developed by the researchers into three types, namely parametric regression, nonparametric regression, and semiparametric regression. Some nonparametric regression models that are widely used include splines, Fourier series, kernels, wavelets, and so on. Spline is a model that has a very special and very good statistical interpretation and visual interpretation. There are three criteria in the formation of the spline regression model, namely determining the order for the model, the number of knots and the location of the knot placement. Several methods are used to select the optimal knot point in nonparametric spline regression, including Cross Validation (CV), Generalized Cross Validation (GCV) and Unbiased Risk (UBR) methods. The purpose of this study was to examine the selection of optimal knot points using the CV, GCV and UBR methods in a nonparametric spline truncated biresponse model. The case studies in this study are the percentage of poor people and the poverty severity index of districts/cities in East Java Province in 2020. Based on the results of the analysis, it is shown that the GCV method is better at getting the optimal knot point than the CV and UBR methods. The GCV method using three optimal knot points obtained an R2 value of 95.763%.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTSt 519.536 Ayu p-1 2022 |
| Uncontrolled Keywords: | Birespon, Cross Validation (CV), Generalized Cross Validation (GCV), Unbiassed Risk (UBR), Spline Truncated, |
| Subjects: | Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression |
| Divisions: | Faculty of Mathematics, Computation, and Data Science > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Mr. Marsudiyana - |
| Date Deposited: | 27 Apr 2026 09:05 |
| Last Modified: | 27 Apr 2026 09:05 |
| URI: | http://repository.its.ac.id/id/eprint/132925 |
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