Estimasi Bobot Pada Model Semiparametrik Spline Truncated Menggunakan Pendekatan Moving Average

Julita, Jiran Julita (2026) Estimasi Bobot Pada Model Semiparametrik Spline Truncated Menggunakan Pendekatan Moving Average. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Regresi semiparametrik spline truncated merupakan metode yang menggabungkan komponen parametrik dan nonparametrik dalam satu model, digunakan ketika sebagian bentuk hubungan antara variabel respon dan variabel prediktor diketahui sedangkan sebagian lainnya tidak diketahui. Dalam penerapannya, model ini sering menghadapi permasalahan heteroskedastisitas yang menyebabkan estimator Ordinary Least Squares tidak lagi bersifat Best Linear Unbiased Estimator. Untuk mengatasi masalah tersebut, digunakan metode Weighted Least Squares dengan bobot yang ditentukan melalui pendekatan moving average sehingga mampu mengakomodasi variasi lokal dari varians residual secara adaptif. Penelitian ini bertujuan untuk mengkaji bentuk estimasi bobot pada model regresi semiparametrik spline truncated terbobot menggunakan pendekatan moving average, serta menerapkannya pada data prevalensi stunting di 38 provinsi Indonesia tahun 2024. Variabel yang digunakan meliputi prevalensi stunting sebagai variabel respon, persentase penduduk miskin sebagai komponen parametrik, dan persentase anak umur 12-23 bulan yang menerima imunisasi dasar lengkap sebagai komponen nonparametrik. Berdasarkan hasil uji Glejser, data menunjukkan adanya heteroskedastisitas dengan nilai F-hitung sebesar 2,9517 pada taraf signifikansi 10% sehingga estimasi parameter dilakukan menggunakan metode Weighted Least Squares. Pemilihan titik knot optimal dilakukan menggunakan kriteria Generalized Cross Validation minimum dari seluruh kombinasi jumlah titik knot, orde spline, serta window size yang diuji secara sistematis. Model terbaik diperoleh pada kombinasi tiga titik knot di posisi 51,47%, 62,13%, dan 70,17%, orde 3, dan window size 2 dengan nilai GCV minimum sebesar 14,4882. Model tersebut menghasilkan koefisien determinasi R² sebesar 86,78%, lebih tinggi dibandingkan model regresi linear berganda yang hanya menghasilkan R² sebesar 51,81%. Residual model telah memenuhi asumsi normalitas dan identik yang membuktikan bahwa heteroskedastisitas pada model awal berhasil diatasi oleh metode Weighted Least Squares dengan pendekatan moving average.
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Truncated spline semiparametric regression is a method that combines parametric and nonparametric components in one model, used when some forms of the relationship between the response variable and the predictor variable are known while others are unknown. In its application, this model often faces heteroscedasticity problems that cause the Ordinary Least Squares estimator to no longer be the Best Linear Unbiased Estimator. To overcome this problem, the Weighted Least Squares method is used with weights determined through a moving average approach so that it can accommodate local variations in residual variance adaptively. This study aims to examine the form of weight estimates in the weighted truncated spline semiparametric regression model using a moving average approach, and apply it to stunting prevalence data in 38 Indonesian provinces in 2024. The variables used include stunting prevalence as the response variable, the percentage of poor people as the parametric component, and the percentage of children aged 12-23 months who received complete basic immunization as the nonparametric component. Based on the results of the Glejser test, the data showed heteroscedasticity with an F-value of 2.9517 at a significance level of 10%, so parameter estimation was carried out using the Weighted Least Squares method. The selection of optimal knot points was carried out using the minimum Generalized Cross Validation criteria from all combinations of the number of knot points, spline orders, and window sizes that were tested systematically. The best model was obtained from a combination of three knot points at positions 51.47%, 62.13%, and 70.17%, order 3, and window size 2 with a minimum GCV value of 14.4882. The model produced a determination coefficient R² of 86.78%, higher than the multiple linear regression model which only produced an R² of 51.81%. The residual model has met the assumptions of normality and is identical, proving that heteroscedasticity in the initial model was successfully overcome by the Weighted Least Squares method with a moving average approach.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	GCV, Moving Average, Regresi Semiparametrik, Prevalensi Stunting, Spline Truncated, Weighted Least Squares ==================================================================================================================================================================================== GCV, Moving Average, Semiparametric Regression, Stunting Prevalence, Truncated Spline, Weighted Least Squares.
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression R Medicine > RA Public aspects of medicine > RA0421 Public health. Hygiene. Preventive Medicine
Divisions:	Faculty of Mathematics, Computation, and Data Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	Jiran Julita
Date Deposited:	04 Aug 2026 02:42
Last Modified:	04 Aug 2026 02:42
URI:	http://repository.its.ac.id/id/eprint/142464

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