Model Geographically Weighted Nonparametric Regression dengan Pendekatan Estimator Campuran Spline Truncated dan Deret Fourier

Laome, Lilis (2024) Model Geographically Weighted Nonparametric Regression dengan Pendekatan Estimator Campuran Spline Truncated dan Deret Fourier. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Dalam disertasi ini diteliti tentang model geographically weighted nonparametric regression (GWNR) dengan pendekatan estimator campuran spline truncated dan deret fourier. Model ini merupakan pengembangan GWR dalam regresi nonparametrik dengan estimator campuran spline truncated dan deret fourier yang melibatkan faktor geografis atau spasial. Model GWNR didekati dengan dua komponen estimator regresi nonparametrik. Komponen pertama, kurva regresi didekati dengan estimator spline truncated multivariabel dan komponen kedua didekati dengan estimator deret fourier multivariabel. Selanjutnya dilakukan analisis inferensial dan diterapkan pada data riil. Berdasarkan tujuan penelitian, diperoleh hasil analisis bahwa estimasi parameter pada model GWNR campuran spline truncated dan deret fourier menggunakan metode weighted maximum likelihood estimation (WMLE) telah diperoleh dengan sifat estimator bersifat unbias dan linear terhadap observasi y. Selanjutnya diperoleh statistik uji kesesuaian model GWNR campuran spline truncated dan deret fourier beserta distribusinya. Kemudian dilanjutkan mendapatkan statistik uji serentak parameter model GWNR campuran spline truncated dan deret fourier beserta distribusinya. Penerapan kasus data kemiskinan di Pulau Sulawesi pada model GWNR menggunakan matrik pembobot fixed kernel Gaussian diperoleh hasil uji kesesuaian model tolak artinya model GWNR bisa digunakan pada data kemiskinan di Pulau Sulawesi tahun 2020. Hasil uji serentak menunjukkan terdapat pengaruh variabel prediktor secara serentak mempengaruhi variabel respon. Adapun uji parsial menunjukkan bahwa sebagian besar variabel prediktor, diantaranya: persentase rumah tangga pengguna kayu bakar (X1), persentase rumah tangga tidak mempunyai jamban (X2), persentase rumah tangga dengan sumber air minum layak (X3) dan rata-rata upah bersih karyawan (X4) yang digunakan mempengaruhi presentase kemiskinan di Pulau Sulawesi. Hal ini didukung dengan nilai kebaikan model yang diperoleh sudah baik.
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This dissertation investigates the geographically weighted nonparametric regression (GWNR) model with a mixed estimator approach of truncated spline and fourier series. This model is a development of GWR in nonparametric regression with a mixed estimator of truncated spline and fourier series involving geographic or spatial factors. The GWNR model is approached with two components of a nonparametric regression estimator. The first component, the regression curve is approximated by a multivariable truncated spline estimator and the second component is approximated by a multivariable fourier series estimator. Furthermore, inferential analysis is conducted and applied to real data. Based on the research objectives, the results of the analysis showed that the parameter estimation in the mixed GWNR model of truncated spline and fourier series using the weighted maximum likelihood estimation (WMLE) method has been obtained with the estimator properties are unbiased and linear to the observation y. Furthermore, the fit test statistics of the GWNR model were obtained. Next, we obtained the fit test statistics of the GWNR mixed spline truncated and fourier series model and its distribution. Then proceed to obtain the simultaneous test statistics of the mixed GWNR model parameters of truncated spline and fourier series and their distribution. The application of the case of poverty data on Sulawesi Island in the GWNR model using a fixed kernel Gaussian weighting matrix obtained the results of the model suitability test rejected, meaning that the GWNR model could be used on poverty data on Sulawesi Island in 2020. The simultaneous test results show that there is an effect of the predictor variables simultaneously affecting the response variable. The partial test shows that most of the predictor variables, including: the percentage of households using firewood (X1), the percentage of households without latrines (X2), the percentage of households with decent drinking water sources (X3) and the average net wage of employees (X4) used affect the percentage of poverty in Sulawesi Island. This is supported by the good value of the model obtained.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	geographically weighted nonparametric regression, spline truncated, deret fourier, WMLE, kemiskinan, fourier series, poverty
Subjects:	H Social Sciences > HA Statistics > HA30.6 Spatial analysis H Social Sciences > HA Statistics > HA31.3 Regression. Correlation
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Lilis Laome
Date Deposited:	07 Feb 2024 04:30
Last Modified:	08 Feb 2024 05:21
URI:	http://repository.its.ac.id/id/eprint/106358

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