Application of Kernel Nonparametric Biresponse Regression with the Nadaraya-Watson Estimator in Poverty Analysis  in South Sulawesi

Hartina Husain; Muhammad Rifki Nisardi; Ryo Hartawan Sasolo

doi:10.31764/jtam.v10i1.33543

Application of Kernel Nonparametric Biresponse Regression with the Nadaraya-Watson Estimator in Poverty Analysis in South Sulawesi

Hartina Husain, Muhammad Rifki Nisardi, Ryo Hartawan Sasolo

Abstract

Poverty is a complex social issue that requires in-depth analysis to identify its contributing factors. South Sulawesi, as one of the provinces in Indonesia, continues to face various challenges in poverty alleviation. This study is a quantitative research that aims to model the poverty rate and poverty severity index using a biresponse nonparametric kernel regression with the Nadaraya-Watson estimator and Gaussian kernel function. The analysis is based on 2024 data form the Central Bureau of Statistics (BPS), which includes poverty indicators as response variables and socio-economic factors, processed using R Studio 2025. The nonparametric biresponse kernel regression analysis yielded optimal bandwidths of h_1=0,188; h_2=0,083; h_3=0,159; and h_4=0,028. Model accuracy is demonstrated by a Generalized Cross-Validation (GCV) value of 5.515 and a Mean Squared Error (MSE) of 0.585, indicating high stability and low prediction error. The model demonstrates adaptive accuracy in simultaneously modeling the two response variables and highlights the strength of kernel-based biresponse regression as an evidence-based tool for policymakers to design targeted, region-specific poverty alleviation strategies.

Keywords

Gaussian; Kernel; Nadaraya-Watson; Nonparametric Biresponse Regression; Poverty.

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References

Adrianingsih, N. Y., Dani, A. T. R., Budiantara, I. N., Ull, D. L., & Kosasih, R. A. (2025). A Computatioal Analysis of Kernel-Based Nonparametric Regression Applied to Poverty Data. Mandalika Mathematics and Educations Journal, 7(3), 1336-1347. https://doi.org/http://dx.doi.org/10.29303/jm.v7i3.9802

Afifah, N., Budiantara, I. N., & Latra, I. N. (2017). Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression. Journal of Physics: Conference Series, 855(1), 1–10. https://doi.org/10.1088/1742-6596/855/1/012002

Aliem, M., & Jamil, M. H. (2023). Human Development Analysis on Poverty Alleviation in South Sulawesi During the Covid-19 Pandemic. Journal of Public Administration and …, 5(April), 59–71. https://jurnal.fisip.untad.ac.id/index.php/JPAG/article/view/738%0Ahttps://jurnal.fisip.untad.ac.id/index.php/JPAG/article/download/738/283

Aliu, M. A., Zubedi, F., Yahya, L., & Oroh, F. A. (2022). The Comparison of Kernel Weighting Functions in Geographically Weighted Logistic Regression in Modeling Poverty in Indonesia. Jurnal Matematika, Statistika Dan Komputasi, 18(3), 362–384. https://doi.org/10.20956/j.v18i3.19567

BPS 2024. (2022). Berita Resmi Statistik. Bps.Go.Id, 19(27), 1–5. https://www.bps.go.id/id/pressrelease/2022/11/07/1916/agustus-2022--tingkat-pengangguran-terbuka--tpt--sebesar-5-86-persen-dan-rata-rata-upah-buruh-sebesar-3-07-juta-rupiah-per-bulan.html

Eubank R L. (1999). Spline Smoothing and Nonparametric Regression Second Edition. Marcel Deker. https://doi.org/10.1201/9781482273144

Hidayat, T., Madris, M., & Anwar, A. I. (2023). Influence of Population, Unemployment, and Poverty on Economic Growth in South Sulawesi Province. Pancasila International Journal of Applied Social Science, 1(01), 68–79. https://doi.org/10.59653/pancasila.v1i01.134

Husain, H., Budiantara, I. N., & Zain, I. (2021). Mixed estimator of spline truncated, Fourier series, and kernel in biresponse semiparametric regression model. IOP Conference Series: Earth and Environmental Science, 880(1). https://doi.org/10.1088/1755-1315/880/1/012046

Husain, H., Rahayu, P. I., Nisardi, M. R., Al-Fadhilah, M. A., & Husain, A. (2025). Semiparametric Biresponse Regression Modeling Mixed Spline Truncated, Fourier Series, and Kernel in Predicting Rainfall and Sunshine. Statistics, Optimization & Information Computing, 14(July), 62–76. https://doi.org/10.19139/soic-2310-5070-2166

Kadir, A., Fasiha, A., Ruslan, M., & Ilham, A. (2019). An Analysis On Poverty Inequality In South Sulawesi-Indonesia By Using Importance Performance Analysis (IPA). I-Finance: a Research Journal on Islamic Finance, 5(2), 85-95.http://jurnal.radenfatah.ac.id/indez.php/i-finance

Mardianto, M. F. F., Sediono, Syahzaqi, I., Safitri, S. A. D., & Afifah, N. (2020). Prediction of Indonesia Strategic Commodity Prices during the COVID-19 Pandemic based on a Simultaneous Comparison of Kernel and Fourier Series Estimator. Journal of Southwest Jiaotong University, 55(6), 1–10. https://doi.org/10.35741/issn.0258-2724.55.6.43

Nakarmi, J., Sang, H., & Ge, L. (2021). Variable bandwidth kernel regression estimation. ESAIM - Probability and Statistics, 25(1), 55–86. https://doi.org/10.1051/ps/2021003

Ni’matuzzahroh, L., & Dani, A. T. R. (2024). Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023. Inferensi, 7(2), 73. https://doi.org/10.12962/j27213862.v7i2.20219

Pasarella, M. D., Sifriyani, S., & Amijaya, F. D. T. (2022). Nonparametrik Regression Model Estimation With the Fourier Series the Fourier Series Approach and Its Application To the Accumulative Covid-19 Data in Indonesia. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(4), 1167–1174. https://doi.org/10.30598/barekengvol16iss4pp1167-1174

Pembargi, J. A., Hadijati, M., & Fitriyani, N. (2023). Kernel Nonparametric Regression for Forecasting Local Original Income. Jurnal Varian, 6(2), 119–126. https://doi.org/10.30812/varian.v6i2.2585

Purwanti, E. (2024). Analisis Deskriptif Profil Kemiskinan Indonesia Berdasarkan Data BPS Tahun 2023. AKADEMIK: Jurnal Mahasiswa Humanis, 4(1), 1–10. https://doi.org/10.37481/jmh.v4i1.653

Ramli, M., Budiantara, I. N., & Ratnasari, V. (2023). A method for parameter hypothesis testing in nonparametric regression with Fourier series approach. MethodsX, 11(October), 1–13. https://doi.org/10.1016/j.mex.2023.102468

Rosalina, M., Martha, S., & Imro’ah, N. (2023). Pemodelan Regresi Nonparametrik Birespon Spline pada Persentase Penduduk Miskin dan Indeks Kedalaman Kemiskinan. Buletin Ilmiah Math. Stat. Dan Terapannya (Bimaster), 12(1), 69–78. https://jurnal.untan.ac.id/index.php/jbmstr/article/viewFile/62849/75676596419

Sabar, W., Iwang, B., Islam, U., & Alauddin, N. (2024). Menilai Dinamika Kemiskinan Di Provinsi Sulawesi Selatan Tahun 2005-2023. 4(2), 93–108. https://doi.org/10.24252/best.v4i2.50013

Sadek, A. M., & Mohammed, L. A. (2024). Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression. International Journal on Informatics Visualization, 8(3), 1352–1360. https://doi.org/10.62527/joiv.8.3.2430

Said, M., Padli, F., Zulfadli, M., & Balqis, S. (2022). Mapping the Poverty Rate of The South Sulawesi Region. In SHS Web of Conferences (Vol. 149, p. 01029). EDP Sciences. https://doi.org/10.1051/shsconf/202214901029

Saidi, S., Herawati, N., Nisa, K., & Setiawan, E. (2021). Nonparametric Modeling Using Kernel Method for the Estimation of the Covid-19 Data in Indonesia During 2020. International Journal of Mathematics Trends and Technology, 67(6), 136–144. https://doi.org/10.14445/22315373/ijmtt-v67i6p516

Tenri Ampa, A., Monica, I., Makkulau, Saidi, L. O., & Muhtar, N. (2024). Priestley Chao Estimator in Nonparametric Multivariable Kernel Regression in Estimating The Value of Indonesia’s Balance Trade. ITM Web of Conferences, 58(6), 04002. https://doi.org/10.1051/itmconf/20245804002

Utami, T. W., & Lahdji, A. (2022). Modeling of Local Polynomial Kernel Nonparametric Regression for Covid Daily Cases in Semarang City, Indonesia. Media Statistika, 14(2), 206–215. https://doi.org/10.14710/medstat.14.2.206-215

Vinod, H. D. (2022). Kernel Regression Coefficients for Practical Significance. Journal of Risk and Financial Management, 15(1), 32. https://doi.org/10.3390/jrfm15010032

DOI: https://doi.org/10.31764/jtam.v10i1.33543