Adrianingsih, Narita Yuri (2021) Estimator Campuran Spline Truncated, Kernel, dan Deret Fourier Dalam Regresi Nonparametrik. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Regresi nonparametrik sangat memungkinkan variabel respon mengikuti
kurva yang berbeda antara satu variabel prediktor dengan variabel prediktor
lainnya. Pada regresi nonparametrik terdapat beberapa jenis pendekatan
diantaranya kernel, spline, dan deret Fourier. Tetapi dalam penggunaannya tidak
hanya satu jenis pendekatan saja, melainkan dapat berupa campuran, seperti
campuran spline dan deret Fourier, kernel dan deret Fourier, dan sebagainya. Pada
data berpasangan diasumsikan mengikuti model regresi nonparametrik campuran,
yaitu komponen yang didekati dengan fungsi spline truncated, komponen kurva regresi
yang didekati dengan fungsi kernel, dan komponen kurva regresi yang didekati dengan
fungsi deret Fourier. Errornya diasumsikan berdistribusi normal dengan mean nol
dan varian konstan. Adapun estimatornya dapat diperoleh dengan menggunakan
metode Ordinary Least Square (OLS). Supaya didapatkan model regresi campuran
nonparametrik yang terbaik, maka diperlukan pemilihan banyaknya titik knot,
bandwidth, osilasi yang optimum yang diperoleh dengan mencari Generalized
Cross Validation (GCV) yang terkecil. Hasil penelitian ini adalah rumusan model
estimasi campuran additif spline truncated, kernel, dan deret fourier. Dalam
penerapannya pada data Indeks Pembangunan Manusia di Jawa Timur tahun 2017,
didapatkan model terbaik dengan menggunakan satu variabel prediktor yang
didekati dengan fungsi spline truncated linier, satu variabel prediktor yang didekati
dengan fungsi kernel, dan satu variabel prediktor yang didekati dengan fungsi deret
fourier. Penentuan model terbaik dengan menggunakan nilai GCV minimum yaitu
sebesar 5,26 dengan R2 sebesar 84,97%.
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Nonparametric regression allows the response variable to follow a different
curve between one predictor variable and another. In nonparametric regression,
there are several types of approaches including kernel, spline, and Fourier series.
But in its use it is not only one type of approach, but can be in the form of a mixture,
such as a mixture of a spline and Fourier series, a kernel and a Fourier series, and
so on. In paired data it is assumed to follow a mixed nonparametric regression
model, namely the component that is approached by the spline truncated function,
the component of the regression curve which is approximated by the kernel
function, and the component of the regression curve which is approached by the
Fourier series function. The error is assumed to be normally distributed with zero
mean and constant variance. The estimator can be obtained using the Ordinary Least
Square (OLS) method. In order to obtain the best nonparametric mixed regression
model, it is necessary to select the optimum number of knots, bandwidth, oscillation
points obtained by looking for the smallest Generalized Cross Validation (GCV).
The results of this study are the formulation of an additive mixture estimation model
of the truncated spline, kernel, and Fourier series. In its application to the Human
Development Index data in East Java in 2017, the best model is obtained using one
predictor variable which is approached with a truncated linear spline function, one
predictor variable which is approximated by the kernel function, and one predictor
variable which is approximated by the Fourier series function. Determination of the
best model using the minimum GCV value of 5.26 with R2 of 84.97%.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Regresi Nonparametrik, Spline Truncated, Kernel, Deret Fourier, Indeks Pembangunan Manusia, Fourier Series, Human Development Index, Kernel, Nonparametric Regression, Truncated Spline |
| Subjects: | H Social Sciences > HA Statistics Q Science > Q Science (General) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Narita Yuri Adrianingsih |
| Date Deposited: | 11 Mar 2021 01:46 |
| Last Modified: | 21 Oct 2024 03:22 |
| URI: | http://repository.its.ac.id/id/eprint/84109 |
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