Nur`aini, Rizky (2023) Pengujian Hipotesis Serentak pada Regresi Nonparametrik Campuran Spline Truncated dan Deret Fourier (Studi Kasus: Pemodelan Indeks Pembangunan Manusia Kabupaten/Kota di Jawa Timur Tahun 2020). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Pada analisis regresi, estimasi kurva regresi dapat dilakukan dengan beberapa pendekatan diantaranya yaitu pendekatan parametrik, nonparametrik, dan semiparametrik. Pendekatan nonparametrik digunakan jika bentuk kurva regresi tidak diketahui dan tidak mengikuti suatu pola tertentu. Beberapa pendekatan estimasi parameter model regresi nonparametrik adalah Kernel, Spline, Deret Fourier, dan Wavelets. Dalam penerapannya, tidak semua variabel prediktor mempunyai pola data yang sama, sehingga diperlukan estimator campuran untuk menyelesaikan permasalahan tersebut. Sebagai pengembangan penelitian sebelumnya, akan dilakukan estimasi parameter model regresi nonparametrik campuran spline truncated dan deret fourier dengan menggunakan optimasi Ordinary Least Square (OLS). Selanjutnya, akan dilakukan pengujian hipotesis serentak terhadap parameter model yang dihasilkan. Statistik uji yang digunakan dalam pengujian hipotesis serentak diperoleh dengan menggunakan Likelihood Ratio Test (LRT). Estimasi dan pengujian hipotesis serentak parameter model regresi nonparametrik campuran spline truncated dan deret fourier diterapkan pada data Indeks Pembangunan Manusia di Kabupaten/Kota Jawa Timur tahun 2020.
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In regression analysis, the regression curve estimation can be done with several approaches including parametric, nonparametric, and semiparametric approaches. The nonparametric approach is used if the shape of the regression curve is unknown and does not follow a certain pattern. Several parameter estimation approaches of nonparametric regression models are Kernel, Spline, Fourier Series, and Wavelets. In practice, not all prediktor variables have the same data pattern, so a mixed estimator is needed to solve the problem. As the development of previous research, a mixed nonparametric regression model of spline truncated and fourier series will be estimated using Ordinary Least Square (OLS) optimization. Furthermore, simultaneous hypothesis testing was carried out on the model parameters. The test statistic used in the simultaneous hypothesis testing was obtained using the Likelihood Ratio Test (LRT). Parameter estimation and simultaneous hypothesis testing of the mixed nonparametric regression model of spline truncated and fourier series will be applied to Human Development Index data in East Java Regency/City in 2020.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Regresi Nonparametrik, Spline Truncated, Deret Fourier, OLS, LRT, Nonparametric Regression, Fourier Series |
| Subjects: | H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HA Statistics > HA31.35 Analysis of variance H Social Sciences > HA Statistics > HA31.3 Regression. Correlation H Social Sciences > HA Statistics > HA31.7 Estimation |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Rizky Nur'aini |
| Date Deposited: | 12 Feb 2023 07:01 |
| Last Modified: | 12 Feb 2023 07:01 |
| URI: | http://repository.its.ac.id/id/eprint/97005 |
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