Estimator Deret Fourier Dalam Regresi Semiparametrik

Pane, Rahmawati (2019) Estimator Deret Fourier Dalam Regresi Semiparametrik. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Fokus penelitian ini adalah men dapat kan estimator dan sifat -sifat dari estimator tersebut dalam Regresi S emiparametrik Deret Fourier (RSDF) baik univariabel maupun multivariabel . Deret Fourier yang digunakan dalam penelitian ini terbatas pada fungsi Cosinus dengan osilasi sebanyak tiga buah. Hasil kajian teoritis diterapkan pada pemodelan tingkat kejernihan air minum PDAM Surabaya . Model RSDF dikembangkan dari model regresi semipar ametrik yang memuat komp onen par ametrik dan nonpar ametrik dimana komponen nonpar ametrik berupa Deret Fourier. Dengan demikian e stimator RSDF meliputi komponen parametrik, nonparametrik dan kurva RSDF. Estimator diperoleh dengan menyelesaikan optimasi Penalized Least Square (PLS) . Untuk mendapatkan osilasi optimal dilakukan pemilihan parameter penghalus yang optimal dengan metode Generalized Cross Validation (GCV) . Hasil kajian teoritis diperoleh estimator komponen parametrik merupakan invers dari hasil kali matrik prediktor dengan parameter penghalus, estimator komponen nonparametrik adalah invers dari hasil kali matrik prediktor nonparametrik dengan parameter penghalus optimal, dan estimator kurva regresi RSDF merupakan gabungan dari estimator parametrik dan nonparametrik. Ketiga estimator yang diperol eh merupakan estimator yang bias tetapi merupakan kelas estimator yang linear. Model RSDF diaplikasikan pada data tingkat kejernihan air minum di PDAM Surabaya . Dari 6 (enam) variabel yaitu Aluminium Sulfat, Khlor Cair, Cupri Sulfat, Kaporit, Dukem 108A, dan Kekeruhan air setelah diendapkan dan menggunakan program R diperoleh model terbaik yang mempun yai R 2 sebesar 84% dan GCV minimum sebesar 0,002703 ========== The focus of this study is to obtain an estimator and its properties of these estimators Fourier Series in Semiparametric Regression (RSDF) both for univariable and multivariable. The Fourier series used in this study is limited to the Cosine function with three oscillations. The results of the theoretical study are applied to modeling the level of clarity of drinking water in PDAM Surabaya. The RSDF model was developed from a semiparametric regression model that contains parametric and nonparametric compon ents where the nonparametric component is Fourier Series. Thus the RSDF estimator includes parametric, nonparametric and RSDF curves. The estimator is obtained by completing the Penalized Least Square (PLS) optimization. To obtain optimal oscillation the optimal smoothing parameter is done using the Generalized Cross Validation (GCV) method. Based on the results of theoretical studies obtained parametric component estimator is the inverse of the predictor matrix product with smoothing parameters, nonparamet ric component estimator is the inverse of matrix product nonparametric predictor with optimal smoothing parameter, and RSDF regression curve estimator is a combination of parametric and nonparametric estimators. The three estimators obtained are biased est imators but are linear estimators classes. The RSDF model is applied to data on the level of clarity of drinking water in PDAM Surabaya. Of the 6 (six) variables namely Aluminum Sulphate, Liquid Khlor, Cupri Sulphate, Chlorine, Dukem 108A, and Turbidity of water after being deposited and using the R program the best model has 2 R of 84% and minimum GCV of 0.002703.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: Deret Fourier, Generalized Cross Validation, Penalized Least Square, Regresi Nonparametrik, Regresi Semiparametrik, Fourier series, Generalized Cross Validation, Penalized Least Square, Nonparametric Regression, Semiparametric Regression
Subjects: H Social Sciences > HA Statistics > HA31.3 Regression. Correlation
Q Science > QA Mathematics > QA404 Fourier series
Divisions: Faculty of Mathematics, Computation, and Data Science > Statistics > 49001-(S3) PhD Thesis
Depositing User: Rahmawati Pane
Date Deposited: 19 Feb 2019 08:09
Last Modified: 19 Feb 2019 08:09
URI: http://repository.its.ac.id/id/eprint/62341

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