Estimator Campuran Spline Smoothing Dan Deret Fourier Dalam Regresi Nonparametrik Multivariabel

Mariati, Ni Putu Ayu Mirah (2021) Estimator Campuran Spline Smoothing Dan Deret Fourier Dalam Regresi Nonparametrik Multivariabel. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Peneliti lebih banyak mengembangkan satu tipe estimator dalam regresi nonparametrik. Namun pada kenyataannya, sering ditemui data dengan pola campuran, khususnya pola data yang sebagian berubah-ubah pada sub interval tertentu dan sebagian lagi polanya mengikuti pola berulang pada suatu tren tertentu. Dalam menangani pola campuran tersebut, maka pada disertasi ini mengembangkan metode baru dalam mengestimasi kurva regresi nonparametrik. Metode ini menggabungkan fungsi Spline Smoothing dan Deret Fourier.
Studi teoritis difokuskan pada model estimator dan pengembangan metode untuk memilih parameter penghalus dan parameter osilasi. Model estimator diselesaikan dengan meminimumkan Penalized Least Square (PLS). Pemodelan ini diselesaikan dengan menggunakan dua tahap estimasi yaitu tahap pertama dengan Penalized Least Square (PLS) dan tahap kedua dengan Least Square (LS). Sifat-sifat estimator campuran Spline Smoothing dan Deret Fourier dalam regresi nonparametrik multivariabel merupakan kelas linier dan bias. Pemilihan parameter penghalus dan parameter osilasi untuk model terbaik menggunakan Generalized Cross Validation (GCV). Studi simulasi dilakukan untuk menguji kinerja model estimator campuran Spline Smoothing dan Deret Fourier. Berdasarkan hasil simulasi dapat disimpulkan bahwa semakin besar ukuran sampel dan semakin kecil ukuran varians, semakin baik model yang diperoleh. Analisis data riil yaitu pengeluaran rumah tangga miskin diilustrasikan untuk model model estimator campuran Spline Smoothing dan Deret Fourier. Berdasarkan analisis data riil, estimator campuran Spline Smoothing dan Deret Fourier mampu memodelkan pengeluaran rumah tangga miskin dengan GCVminimum= -13 1,42×10 , R2=98,99%, Mean Square Error (MSE) didapat -5 8,66×10 .
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More researchers develop one type of estimator in nonparametric regression. But in fact, it is often encountered data with mixed patterns, especially data patterns that partially change at certain sub-intervals and partially follow a repeating pattern in a certain trend. In dealing with this mixed pattern, this dissertation develops a new method for estimating nonparametric regression curves. This method combines the Spline Smoothing and Fourier Series functions. Theoretical studies are focused on estimator models and the development of methods for selectingsmoothing parameters and oscillation parameters. The estimator model is solved by minimizing the Penalized Least Square (PLS). This modeling was completed using two stages of estimation, namely the first stage with the Penalized Least Square (PLS) and the second stage with the Least Square (LS). The mixed estimator properties of Spline Smoothing and Fourier Series in multivariable nonparametric regression are linear and biased classes. Selection of smoothing parameters and oscillation parameters for the best model uses Generalized Cross Validation (GCV).
A simulation study was conducted to test the performance of the Spline Smoothing and Fourier Series estimator models. Based on the simulation results, it can be concluded that the larger the sample size and the smaller the variance, the better the model obtained. The real data analysis, namely the expenditure of poor households, is illustrated for the mixed spline smoothing estimator model and the Fourier series. Based on real data analysis, the estimator of the mixture Spline Smoothing and Fourier Series is able to model the expenditure of poor households with GCVminimum= -13 1,42×10 , R2=98,99%, Mean Square Error (MSE) value is obtained -5 8,66×10 .

Item Type:	Thesis (Doctoral)
Additional Information:	RDSt 519.536 Mar e-1
Uncontrolled Keywords:	Estimator Campuran, Regresi Nonparametrik, Spline Smoothing, Deret Fourier, Rumah Tangga Miskin
Subjects:	Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	- Davi Wah
Date Deposited:	05 Jun 2023 04:02
Last Modified:	05 Jun 2023 05:15
URI:	http://repository.its.ac.id/id/eprint/98035

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