Sudiarsa, I Wayan (2018) ESTIMATOR GABUNGAN DERET FOURIER DAN SPLINE TRUNCATED DALAM REGRESI NONPARAMETRIK MULTIVARIABEL. Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Salah satu permasalahan yang muncul dalam kehidupan sehari-hari adalah bagaimana menjelaskan hubungan antara suatu respon dengan beberapa prediktor. Analisis regresi merupakan metode statistika yang digunakan untuk mengestimasi pola hubungan antara respon (y) dengan prediktor (x). Pengembangan regresi nonparametrik deret Fourier yang melibatkan beberapa prediktor, selama ini lebih banyak dikembangkan untuk prediktor yang polanya sama. Perlu dikembangkan estimator yang polanya berbeda untuk beberapa prediktor pada regresi nonparametrik multivariabel. Penelitian teoritis akan difokuskan pada bentuk estimator, dan pengembangan metode untuk memilih parameter penghalus yang optimal pada estimator deret Fourier dan truncated spline. Hasil teoritis diaplikasikan pada data simulasi dan data produksi padi di Provinsi Bali tahun 2015. Estimasi fungsi regresi gabungan deret Fourier dan truncated spline, diperoleh melalui optimasi penalized least squares (PLS). Estimasi fungsi kurva regresi memuat estimator dan titik knot. Berdasarkan hasil simulasi diperoleh bahwa semakin besar ukuran sampel dan semakin kecil ukuran varians, maka akan menghasilkan nilai estimasi parameter dan knot yang semakin baik. Pemodelan produksi padi di Provinsi Bali menggunakan estimator gabungan deret Fourier dan spline truncated terbaik mempunyai GCV minimum 668466,65 dan R2 = 97,22%. Model gabungan deret Fourier dan spline truncated sangat sesuai untuk memodelkan produksi padi di Provinsi Bali. ======== One of the problems in life is how to explain the relationship between a response with some predictors. Regression analysis is a statistical used to estimate the relation pattern between response (y) with predictor (x). The development of Fourier series in nonparametric regression involving multiple predictors has been developed for predictors of the same pattern. We need to develop estimators for different predictors of multivariable nonparametric regression. Theoretical research will be focused on the estimator and the development of methods to select the optimal parameters in estimators the fourier series and truncated spline. The results theoretical is were applied to simulation data and real data rice production in Bali Province (2015). Estimation of combined nonparametric regression of fourier series and truncated spline was obtained by optimized penalized least squares (PLS). Estimation of regression curve function contains estimator and knot point. Based on the simulation results obtained that larger the sample size and smaller the size of the variance, it will result in better parameter estimation values and knots. The modeling of rice production in Province Bali using the combined estimator of fourier series and spline truncated has a minimum GCV of 668466.65 and R2 = 97,22%. Combined models fourier series and spline truncated are well suited to model rice production in Bali Province.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Additional Information: | RDSt 519.536 Sud e |
| Uncontrolled Keywords: | Deret Fourier, Truncated Spline, Regresi Nonparametrik, Multivariabel, Penalized Least Squares (PLS) |
| Subjects: | Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression |
| Divisions: | Faculty of Mathematics, Computation, and Data Science > Statistics > 49001-(S3) PhD Thesis |
| Depositing User: | SUDIARSA I WAYAN |
| Date Deposited: | 12 Oct 2020 03:32 |
| Last Modified: | 12 Oct 2020 03:32 |
| URI: | http://repository.its.ac.id/id/eprint/59424 |
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