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 mendapatkan estimator dan sifat-sifat dari
estimator tersebut dalam Regresi Semiparametrik 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 semiparametrik yang
memuat komponen parametrik dan nonparametrik dimana komponen
nonparametrik berupa Deret Fourier. Dengan demikian estimator 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 diperoleh 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 mempunyai R2 sebesar
84% dan GCV minimum sebesar 0,002703.
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Fourier Series Estimator In Semiparametric Regression
ABSTRACT
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 components 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, nonparametric 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 estimators 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)
Additional Information:	RDSt 519.536 Pan e-1 2019
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 > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA404 Fourier series
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Rahmawati Pane
Date Deposited:	19 Feb 2019 08:09
Last Modified:	11 Apr 2022 07:55
URI:	http://repository.its.ac.id/id/eprint/62341

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