PERFORMANCE COMPARISON OF SEMIPARAMETRIC KERNEL REGRESSION USING EPANECHNIKOV, GAUSSIAN, AND, BIWEIGHT KERNELS IN MODELING LIFE EXPECTANCY IN INDONESIA

Authors

  • Cinta Rizki Oktarina Institut Teknologi Batam
  • Sigit Nugroho Universitas Bengkulu
  • Idhia Sriliana Universitas Bengkulu
  • Putri Suci Aria Department of Mathematics, Faculty of Information Technology, Batam Institute of Technology, Batam, Indonesia

DOI:

https://doi.org/10.25077/jmua.15.3.406-417.2026

Keywords:

Bandwidth Selection, Life Expectancy, Semiparametric Kernel Regression

Abstract

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.

Downloads

Download data is not yet available.

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.

Downloads

Published

31-07-2026

How to Cite

Oktarina, C. R., Nugroho, S., Sriliana, I., & Suci Aria, P. (2026). PERFORMANCE COMPARISON OF SEMIPARAMETRIC KERNEL REGRESSION USING EPANECHNIKOV, GAUSSIAN, AND, BIWEIGHT KERNELS IN MODELING LIFE EXPECTANCY IN INDONESIA. Jurnal Matematika UNAND, 15(3), 406–417. https://doi.org/10.25077/jmua.15.3.406-417.2026

Issue

Vol. 15 No. 3 (2026)

Section

Articles

License

Copyright (c) 2026 Departemen Matematika dan Sains Data FMIPA UNAND

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0). This license allows published content to be freely accessed, shared, redistributed, and adapted for any purpose, including commercial use, provided that the applicable license conditions are followed.

Copyright Holder

The copyright of articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND), in accordance with the journal's stated copyright policy.

Author Rights

Under the CC BY-SA 4.0 license, authors may share, distribute, and reuse their published articles, subject to the applicable license conditions. These rights include:

  • Self-Archiving: Authors may deposit their published articles in institutional repositories, personal websites, or academic platforms.

  • Reuse: Authors may reuse their published work in subsequent publications, research, teaching materials, or other lawful purposes, provided that appropriate attribution is maintained.

  • Distribution: Authors may share and distribute their published articles without requiring additional permission under the terms of the license.

Creative Commons License (CC BY-SA 4.0)

Under the CC BY-SA 4.0 license, users are free to:

  • Share: Copy and redistribute the material in any medium or format.

  • Adapt: Remix, transform, and build upon the material for any purpose, including commercial purposes.

These permissions are subject to the following conditions:

  • Attribution: Users must give appropriate credit to the original author(s), retain relevant copyright notices, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author(s), copyright holder, or journal.

  • ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same CC BY-SA 4.0 license or a compatible license.

  • No Additional Restrictions: Users may not apply legal terms or technological measures that legally restrict others from exercising the rights granted by the license.

For more information about the CC BY-SA 4.0 license, please visit:

https://creativecommons.org/licenses/by-sa/4.0/

Third-Party Content

Third-party materials, including figures, tables, photographs, and illustrations, are covered by the article's CC BY-SA 4.0 license only when their inclusion under that license is authorized.

Materials excluded from the license must be clearly identified with appropriate copyright notices and attribution. Authors are responsible for obtaining any necessary permissions, while users must comply with the applicable licensing terms or permissions when reusing excluded materials.

Copyright and Licensing Information

Copyright and licensing information should be clearly displayed on each published article's landing page and included in the full-text versions (HTML and PDF), where applicable, to ensure transparency regarding copyright ownership and permitted reuse.