Pemodelan Regresi Nonparametrik dengan Estimator Spline Truncated vs Deret Fourier

Andrea Tri Rian Dani; Narita Yuri Adrianingsih

doi:10.34312/jjom.v3i1.7713

Pemodelan Regresi Nonparametrik dengan Estimator Spline Truncated vs Deret Fourier

Andrea Tri Rian Dani, Narita Yuri Adrianingsih

Abstract

ABSTRAK

Pendekatan regresi nonparametrik digunakan apabila hubungan antara variabel prediktor dan variabel respon tidak diketahui polanya. Spline truncated dan deret Fourier merupakan estimator dalam pendekatan nonparametrik yang terkenal, karena memiliki fleksibilitas yang tinggi dan mampu menyesuaikan terhadap sifat lokal data secara efektif. Penelitian ini bertujuan untuk mendapatkan estimator model regresi nonparametrik terbaik menggunakan spline truncated dan deret Fourier. Metode estimasi kurva regresi nonparametrik dilakukan dengan menyelesaikan optimasi Ordinary Least Squares (OLS). Kriteria kebaikan model menggunakan GCV, R² dan MSE. Pemodelan regresi nonparametrik diterapkan pada data Case Fatality Rate (CFR) akibat Demam Berdarah Dengue (DBD) di Indonesia. Berdasarkan hasil analisis, hasil estimasi dari pemodelan regresi nonparametrik menunjukkan bahwa estimator spline truncated memberikan performa yang lebih baik dibandingkan estimator deret Fourier. Hal ini ditunjukkan dengan nilai R²dari estimator spline truncated yaitu sebesar 91,80% dan MSE sebesar 0,04, sedangkan dengan estimator deret Fourier diperoleh nilai R² sebesar 65,44% dan MSE sebesar 0,19.

ABSTRACT

The nonparametric regression approach is used when the relationship between the predictor variable and the response variable is unknown. Spline truncated and Fourier series are well-known estimators in the nonparametric approach because they have high flexibility and are able to adjust to the local properties of the data effectively. This study aims to obtain the best nonparametric regression model estimator using the truncated spline and the Fourier series. The nonparametric regression curve estimation method is done by completing the Ordinary Least Squares (OLS) optimization. The criteria for the goodness of the model use GCV, R², and MSE. Nonparametric regression modeling is applied to Case Fatality Rate (CFR) modeling due to Dengue Hemorrhagic Fever (DBD) in Indonesia. Based on the analysis, the estimation results from the nonparametric regression modeling show that the truncated spline estimator provides better performance than the Fourier series estimator. This is shown by the R² value of the truncated spline estimator which is 91.80% and the MSE is 0.04, while the Fourier series estimator obtained an R² value of 65.44% and MSE of 0.19.

Keywords

Regresi Nonparametrik; Spline Truncated; Deret Fourier

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DOI: https://doi.org/10.34312/jjom.v3i1.7713