Ampa, Andi Tenri (2023) Estimator Campuran Kernel Dan Deret Fourier Multivariabel Dalam Regresi Semiparametrik. Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Model regresi gabungan Kernel dan deret Fourier multivariabel dalam regresi semiparametrik dikembangkan dari model regresi semiparametrik yang mengandung komponen parametrik dan nonparametrik. Komponen nonparametrik menggunakan estimator gabungan dari estimator Kernel multivariabel dan estimator Deret Fourier multivariabel. Estimator diperoleh dengan menyelesaikan optimasi Penalized Least Square (PLS). Selanjutnya karena kebaikan estimator yang didapat tergantung dari parameter penghalus optimal, parameter bandwidth optimal dan parameter osilasi optimal, maka penelitian ini juga mengembangkan metode pemilihan parameter smoothing optimal, bandwidth optimal dan parameter osilasi optimal menggunakan Generalized Cross Validation (GCV) metode. Model terbaik diperoleh pada nilai GCV minimum. Metode penelitian yang digunakan adalah studi literatur dan studi teoritis serta aplikasi pada data real. Hasil studi literatur dan studi teoritis diperoleh estimator kurva regresi campuran Kernel dan deret Fourier multivariabel dalam regresi semiparametrik. Estimator ini menggabungkan kebaikan dari estimator parametrik, estimator deret Fourier dan estimator Kernel, selain itu memiliki komponen parametrik multivariabel, nonparametrik Kernel multivariabel dan nonparametrik deret Fourier multivariabel sehingga estimator ini baik dan penggunaannya lebih fleksibel dalam hal jumlah variabel. Estimator yang diperoleh tidak bias asimptotik, dan termasuk dalam kelas estimator linier. Model campuran Kernel dan Deret Fourier diaplikasi pada Data Produksi Padi di Provinsi Bali dengan unit pengamatan 57 kecamatan. Variabel yang dilibatkan yaitu luas lahan panen, curah hujan, suhu udara dan kecepatan angin. Model campuran Kernel dan Deret Fourier dalam regresi semiparametrik yang memiliki nilai GCV terkecil= 1,2457 melibatkan variabel luas lahan panen yang didekati dengan fungsi linier, curah hujan dan suhu udara keduanya didekati dengan fungsi Deret Fourier, sedangkan variabel kecepatan angin didekati dengan Kernel
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Kernel combined regression model and multivariable Fourier series in semiparametric regression developed from a semiparametric regression model that contains parametric and nonparametric components. The nonparametric component uses a combined estimator of the multivariable Kernel estimator and the multivariable Fourier Series estimator. The estimator is obtained by completing the Penalized Least Square (PLS) optimization. Furthermore, because the goodness of the estimator obtained depends on the optimal smoothing parameters, optimal bandwidth parameters and optimal oscillation parameters, this research also develops a method for selecting optimal smoothing parameters, optimal bandwidth and optimal oscillation parameters using the Generalized Cross Validation (GCV) method. The best model is obtained at the minimum GCV value. The research method used is a literature study and theoretical studies as well as applications to real data. The results of literature studies and theoretical studies obtained the Kernel mixed regression curve estimator and multivariable Fourier series in semiparametric regression. This estimator combines the goodness of parametric estimators, Fourier series estimators and Kernel estimators, besides that it has multivariable parametric components, multivariable nonparametric Kernel and nonparametric multivariable Fourier series so that this estimator is good and its use is more flexible in terms of the number of variables. The estimator obtained is asymptotically unbiased, and belongs to the class of linear estimators. The Kernel mixed model and Fourier series were applied to rice production data in the Province of Bali with a unit of observation of 57 sub-districts. The variables involved were harvested land area, rainfall, air temperature and wind speed. The mixed model of the Kernel and Fourier series in semiparametric regression which has the smallest GCV value = 1.2457 involves the variable area of harvested land which is approximated by a linear function, rainfall and air temperature are both approximated by a Fourier series function, while the wind speed variable is approximated by the Kernel.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Uncontrolled Keywords: | Deret Fourier, Generalized Cross Validation, semiparametrik, Penalized Least Square, kernel. |
| Subjects: | Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA353.K47 Kernel functions (analysis) Q Science > QA Mathematics > QA401 Mathematical models. Q Science > QA Mathematics > QA404 Fourier series Q Science > QA Mathematics > QA76.6 Computer programming. Q Science > QA Mathematics > QA76.9.D343 Data mining. Querying (Computer science) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis |
| Depositing User: | Andi Tenri Ampa |
| Date Deposited: | 02 Mar 2023 07:28 |
| Last Modified: | 07 Mar 2023 01:59 |
| URI: | http://repository.its.ac.id/id/eprint/97728 |
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