PERFORMANCE COMPARISON OF SEMIPARAMETRIC KERNEL REGRESSION USING EPANECHNIKOV, GAUSSIAN, AND, BIWEIGHT KERNELS IN MODELING LIFE EXPECTANCY IN INDONESIA
DOI:
https://doi.org/10.25077/jmua.15.3.406-417.2026Keywords:
Bandwidth Selection, Life Expectancy, Semiparametric Kernel RegressionAbstract
Life expectancy is a crucial indicator of population health and socioeconomic development, and its relationship with explanatory variables often exhibits both linear and nonlinear patterns. This study employs a semiparametric kernel regression approach to model life expectancy in Indonesia by integrating parametric and nonparametric components. Undernutrition is modeled parametrically, while access to improved drinking water and the illiteracy rate are treated as nonparametric predictors to flexibly capture their nonlinear effects. The nonparametric component is estimated using the Nadaraya–Watson kernel estimator, whereas parameter estimation is conducted using the Ordinary Least Squares method. Several kernel functions are evaluated, and the optimal kernel and bandwidth are selected based on the minimum Generalized Cross-Validation (GCV) criterion. The results indicate that the Gaussian kernel with an optimal bandwidth of (100, 100) yields the best performance. The proposed model demonstrates excellent accuracy, with a coefficient of determination of 99.99% and a very low Root Mean Square Error (RMSE). These findings confirm that semiparametric kernel regression is a flexible and reliable method for modeling life expectancy and other public health indicators characterized by complex relationships.
References
[1] Pahlepi, R., Sriliana, I., Agwil, W., & Oktarina, C. R. (2025). Biresponse truncated spline nonparametric regression modeling for longitudinal data on monthly stock prices of three private banks in Indonesia. Barekeng, 19, 2467–2480.
[2] Budiantara, I. N. (2019). Regresi nonparametrik spline truncated. Surabaya: ITS Press.
[3] Yang, S., Liu, J., Du, P., Wu, J., & Wan, L. (2025). Semiparametric approach for dual-response robust design with complex two-factor interactions. Quality Engineering, 1–23.
[4] Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression. Cambridge: Cambridge University Press.
[5] Fan, J., & Gijbels, I. (1996). Local polynomial modelling and its applications. Monographs on Statistics and Applied Probability, Vol. 66. London: Chapman & Hall.
[6] Oktarina, C. R., Nugroho, S., Sriliana, I., Novianti, P., Sunandi, E., & Pahlepi, R. (2025). Estimation of stunting and wasting in Sumatra 2022 with Nadaraya–Watson kernel and penalized spline. Inferensi, 8, 197–?. Online ISSN: 2721-3862.
[7] Kahar, A. M., Suparti, & Hakim, A. R. (2023). Analisis indeks harga saham gabungan dan faktor pengaruhnya menggunakan pemodelan regresi semiparametrik kernel dilengkapi GUI-R. Jurnal Gaussian, 12, 30–41.
[8] Era, Rizki, S. W., & Yundari. (2022). Pemodelan indeks harga saham gabungan dengan model regresi semiparametrik kernel. Equator: Journal of Mathematical and Statistical Sciences, 1.
[9] Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis (6th ed.). Hoboken, NJ: John Wiley & Sons.
[10] Freund, R. J., & Wilson, W. J. (2003). Statistical methods (2nd ed.). San Diego: Academic Press (Elsevier).
[11] Gujarati, D. N. (2015). Econometrics by example (2nd ed.). London: Palgrave Macmillan.
[12] Eubank, R. L. (1999). Nonparametric regression and spline smoothing (2nd ed.). New York: Marcel Dekker.
[13] Wang, Y. (2011). Smoothing splines: Methods and applications. Boca Raton: CRC Press.
[14] Ali, T. H. (2019). Modification of the adaptive Nadaraya–Watson kernel method for nonparametric regression. Communications in Statistics – Simulation and Computation, 51, 391–403.
[15] Ali, T. H., Hayawi, H. A. A. M., & Botani, D. S. I. (2021). Estimation of the bandwidth parameter in Nadaraya–Watson kernel nonparametric regression based on universal threshold level. Communications in Statistics – Simulation and Computation, 52, 1476–1489.
[16] Guidoum, A. (2020). Kernel estimator and bandwidth selection for density and its derivatives: The kedd package. arXiv preprint, arXiv:2012.06102, 1–22.
[17] Sriliana, I., Budiantara, I., & Ratnasari, V. (2024). The performance of mixed truncated spline–local linear nonparametric regression model for longitudinal data. MethodsX, 12, 102652.
[18] Härdle, W., & Barry, D. (1994). Applied nonparametric regression. Cambridge: Cambridge University Press.
[19] Suparti, Santoso, R., Prahutama, A., et al. (2017). Regresi nonparametrik (1st ed.). Ponorogo: Wade Group.
[20] Oktarina, C. R., Sriliana, I., & Nugroho, S. (2025). Penalized spline semiparametric regression for bivariate response in modeling macro poverty indicators. Indonesian Journal of Applied Statistics, 8, 13–23.
[21] Alwi, W., Sauddin, A., & Islamiah, N. M. (2023). Faktor-faktor yang mempengaruhi angka harapan hidup di Sulawesi Selatan menggunakan analisis regresi. Jurnal Matematika dan Statistika serta Aplikasinya, 11, 72–80.
[22] Tanadjaja, A., Zain, I., & Wibowo, W. (2017). Pemodelan angka harapan hidup di Papua dengan pendekatan geographically weighted regression. Jurnal Sains dan Seni ITS, 6, D82–D87.
[23] Amalia, N., & Mahmudah. (2020). Faktor yang mempengaruhi angka harapan hidup di Provinsi Jawa Timur tahun 2014 dengan melihat nilai statistik Cp Mallows. Jurnal Wiyata, 7, 13–14.
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