Estimasi Matriks Varian Kovarian Pada Estimator Campuran Spline Truncated, Kernel, Dan Deret Fourier Dalam Regresi Semiparametrik Birespon

Aisy, Umniyah Rihadatul (2022) Estimasi Matriks Varian Kovarian Pada Estimator Campuran Spline Truncated, Kernel, Dan Deret Fourier Dalam Regresi Semiparametrik Birespon. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Analisis regresi merupakan analisis dalam statistika yang digunakan untuk menyelidiki pola hubungan antara variabel respon dengan variabel prediktor. Terdapat tiga pendekatan dalam analisis regresi, diantaranya regresi parametrik, regresi nonparametrik, dan regresi semiparametrik. Apabila pola data diketahui, maka pendekatan analisis regresi yang digunakan adalah regresi parametrik. Sedangkan, regresi nonparametrik merupakan pendekatan dalam analisis regresi untuk mengetahui model hubungan antara variabel prediktor dengan variabel respon dimana pola datanya tidak diketahui. Pendekatan yang ketiga adalah regresi semiparametrik yang merupakan kombinasi antara regresi parametrik dan regresi nonparametrik. Adapun beberapa komponen nonparametrik yang sering digunakan adalah spline truncated, kernel, dan deret fourier. Selain dibedakan ke dalam tiga pendekatan, analisis regresi juga dibedakan pada banyaknya respon yang digunakan, apabila model regresi memiliki dua variabel respon dan antar responnya saling berkorelasi, maka disebut regresi birespon. Secara teoritis, representasi hubungan antar respon tersebut dinyatakan dalam matriks varian kovarian yang digunakan sebagai pembobot dalam estimator parameter pada model regresi. Hingga saat ini, belum banyak penelitian mengenai matriks varian kovarian untuk mengakomodasi adanya korelasi antar variabel respon pada estimator campuran dalam regresi semiparametrik birespon. Penelitian ini bertujuan untuk menentukan estimasi matriks varian kovarian dalam tiga estimator campuran yaitu spline truncated, kernel, dan deret fourier pada regresi semiparametrik birespon menggunakan metode maximum likelihood (MLE). Hasil estimasi matriks varian kovarian tersebut digunakan untuk membentuk model regresi semiparametrik birespon yang diimplementasikan pada data produksi padi dan PDRB sektor pertanian di Provinsi Jawa Tengah tahun 2019. Dalam menentukan model terbaik, digunakan nilai GCV terkecil, dimana model terbaik yang diperoleh merupakan model dengan variabel luas lahan sawah didekati dengan komponen parametrik, curah hujan didekati dengan spline truncated, jumlah tenaga kerja didekati dengan et fourier, dan untuk penggunaan pupuk didekati dengan kernel. Model terbaik tersebut menggunakan 1 knot 1 osilasi dengan nilai GCV sebesar 1.7825, sebesar 86.55%, dan MSE sebesar 1.5316.
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Regression analysis is an analysis in statistics that is used to investigate the pattern of relationships between response variables and predictor variables. There are three approaches in regression analysis, including parametric regression, nonparametric regression, and semiparametric regression. If the data pattern is known, the regression analysis approach used is parametric regression. Meanwhile, nonparametric regression is an approach in regression analysis to determine the model of the relationship between predictor variables and response variables where the data pattern is unknown. The third approach is semiparametric regression which is a combination of parametric regression and nonparametric regression. The nonparametric components that are often used are truncated splines, kernels, and Fourier series. In addition to being divided into three approaches, regression analysis is also distinguished by the number of responses used, if the regression model has two response variables and the responses are correlated, it is called biresponse regression. Theoretically, the representation of the relationship between the responses is expressed in the variance-covariance matrix which is used as weights in the parameter estimator in the regression model. Until now, there have not been many studies on the variance-covariance matrix to accommodate the correlation between response variables in mixed estimators in biresponse semiparametric regression. This study aims to determine the estimation of the variance-covariance matrix in three mixed estimators, namely, spline truncated, kernel, and Fourier series in biresponse semiparametric regression using the maximum likelihood (MLE) method. The estimation results of the variance-covariance matrix are used to form a biresponse semiparametric regression model which is implemented in the data of rice production and GRDP of the agricultural sector in Central Java Province in 2019. In determining the best model, the smallest GCV value is used, where the best model obtained is a model with paddy land area variables were approximated by parametric components, rainfall was approximated by spline truncated, the amount of labor was approximated by the Fourier series, and the quantity of fertilizers was approximated by the kernel. The best model uses 1 knot 1 oscillation with a GCV value of 1.7825, of 86.55%, and an MSE of 1.5316.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Variance-covariance Matrix, Biresponse Semiparametric Regression, Spline Truncated, Kernel, Fourier Series,Matriks Varian Kovarian, Regresi Semiparametrik Birespon, Spline Truncated, Kernel, Deret Fourier.
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA353.K47 Kernel functions (analysis) Q Science > QA Mathematics > QA404 Fourier series
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Umniyah Rihadatul Aisy
Date Deposited:	19 Feb 2022 21:14
Last Modified:	31 Oct 2022 01:39
URI:	http://repository.its.ac.id/id/eprint/94641

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