Estimation of Stunting and Wasting in Sumatra 2022 with Nadaraya-Watson Kernel and Penalized Spline

Cinta Rizki Oktarina, Sigit Nugroho, Idhia Sriliana, Pepi Novianti, Etis Sunandi, Reza Pahlepi

Abstract


This study aims to estimate the prevalence of Stunting and Wasting in Sumatra in 2022 using nonparametric regression methods, specifically the Nadaraya-Watson Kernel and Penalized Spline regression models. Both models were applied to assess the relationship between these two correlated response variables and various predictor variables, such as low birth weight, sanitary facilities, poor population, and exclusive breastfeeding. The results showed that the Nadaraya-Watson Kernel regression, particularly using the Gaussian kernel, provided the best fit with minimal prediction error, as indicated by its low Generalized Cross-Validation (GCV) value of 0.024 and high R-squared values (0.9992 for Stunting and 0.9995 for Wasting). In contrast, the Epanechnikov kernel and Biweight kernel produced higher GCV values (0.110 and 0.356, respectively), indicating less optimal performance. For the Penalized Spline model, optimal parameters were determined with a smoothing parameter λ of 5 and 3 knots, which balanced model flexibility and smoothness. This research underscores the potential of nonparametric regression techniques in capturing complex relationships in health data and provides insights for improving interventions aimed at addressing child malnutrition in Indonesia.

Keywords


Kernel; Nonparametric Birespon Regression; Penalized Spline; Stunting; Wasting

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References


R. L. Eubank, Nonparametric Regression and Spline Smoothing. New York: Marcel Dekker, Inc, 1999.

P. P. Gabrela, J. D. T. Purnomo, and I. N. Budiantara, “The Estimation of Mixed Truncated Spline and Fourier Series Estimator in Bi-Response Nonparametric Regression,” AIP Conf. Proc., vol. 2903, no. 1, 2023, doi: 10.1063/5.0177224.

I. Sriliana, I. N. Budiantara, and V. Ratnasari, “The Performance of Mixed Truncated Spline-Local Linear Nonparametric Regression Model for Longitudinal Data,” MethodsX, vol. 12, no. July 2023, 2024, doi: 10.1016/j.mex.2024.102652.

R. Hidayat, I. N. Budiantara, B. W. Otok, and V. Ratnasari, “The regression curve estimation by using mixed smoothing spline and kernel (MsS-K) model,” Commun. Stat. - Theory Methods, vol. 50, no. 17, pp. 3942–3953, 2021, doi: 10.1080/03610926.2019.1710201.

T. H. Ali, H. A. A. M. Hayawi, and D. S. I. Botani, “Estimation of the bandwidth parameter in Nadaraya-Watson kernel Non-Parametric Regression Based on Universal Threshold Level,” Commun. Stat. Simul. Comput., vol. 52, no. 4, pp. 1476–1489, 2021, doi: 10.1080/03610918.2021.1884719.

G. Yang, B. Zhang, and M. Zhang, “Estimation of Knots in Linear Spline Models,” J. Am. Stat. Assoc., vol. 118, no. 541, pp. 639–650, 2023, doi: 10.1080/01621459.2021.1947307.

D. Barry and W. Hardle, Applied Nonparametric Regression., 1st ed. Cambridge University Press., 1994. doi: 10.2307/2982873.

C. R. Oktarina, I. Sriliana, and S. Nugroho, “Penalized Spline Semiparametric Regression for Bivariate Response in Modeling Macro Poverty Indicators,” Indones. J. Appl. Stat., vol. 8, no. 1, pp. 13–23, 2025, doi: https://doi.org/10.13057/ijas.v8i1.94370.

K. Xie, F. Meng, and D. Zhang, “Regional Forecasting of PM2.5 Concentrations: A Novel Model Based on The Empirical Orthogonal Function Analysis and Nadaraya–Watson Kernel Regression Estimator,” Environ. Model. Softw., vol. 170, no. January, p. 105857, 2023, doi: 10.1016/j.envsoft.2023.105857.

A. R. Fadilah, A. Fitrianto, and I. M. Sumertajaya, “Outlier Identification on Penalized Spline Regression Modeling for Poverty Gap Index in Java,” BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 4, pp. 1231–1240, 2022, doi: 10.30598/barekengvol16iss4pp1231-1240.

M. Blössner and M. de Onis, “Malnutrition Quantifying the Health Impact at National and Local Levels,” 12th ed., no. 12, Geneva: World Health Organization, 2005.

I. N. Budiantara, Regresi Nonparametrik Spline Truncated. Surabaya: ITS Press, 2019.

D. Ruppert, M. P. Wand, and R. . Carroll, Semiparametric Regression. Cambridge University Press, 2003. doi: 10.1201/9781420091984-c17.

Q. Yang, Q. Kang, Q. Huang, Z. Cui, Y. Bai, and H. Wei, “Linear correlation analysis of ammunition storage environment based on Pearson correlation analysis,” J. Phys. Conf. Ser., vol. 1948, no. 1, 2021, doi: 10.1088/1742-6596/1948/1/012064.

Sifriyani, A. R. M. Sari, A. T. R. Dani, and S. Jalaluddin, “Bi-Response Truncated Spline Nonparametric Regression With Optimal Knot Point Selection Using Generalized Cross-Validation in Diabetes Mellitus Patient’S Blood Sugar Levels,” Commun. Math. Biol. Neurosci., vol. 2023, pp. 1–18, 2023, doi: 10.28919/cmbn/7903.

S. Tosatto, R. Akrour, and J. Peters, “An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression Under Lipschitz Assumptions,” Stats, vol. 4, no. 1, pp. 1–17, 2021, doi: 10.3390/stats4010001.

L. Selk and J. Gertheiss, “Nonparametric Regression and Classification with Functional, Categorical, and Mixed Covariates,” Adv. Data Anal. Classif., vol. 17, no. 2, pp. 519–543, 2022, doi: 10.1007/s11634-022-00513-7.

T. Misiakiewicz and B. Saeed, “A non-Asymptotic Theory of Kernel Ridge Regression: Deterministic Equivalents, Test Error, and GCV Estimator,” pp. 1–131, 2024, [Online]. Available: http://arxiv.org/abs/2403.08938

L. Yang and Y. Hong, “Adaptive Penalized Splines for Data Smoothing,” Comput. Stat. Data Anal., vol. 108, pp. 70–83, 2017, doi: 10.1016/j.csda.2016.10.022.

X. Li et al., “A Practical and Effective Regularized Polynomial Smoothing (RPS) Method for High-Gradient Strain Field Measurement In Digital Image Correlation,” Opt. Lasers Eng., vol. 121, no. April, pp. 215–226, 2019, doi: 10.1016/j.optlaseng.2019.04.017.

R. Pahlepi, I. Sriliana, W. Agwil, and C. R. Oktarina, “Biresponse Spline Truncated Nonparametric Regression Modeling for Longitudinal Data on Monthly Stock Prices of Three Private Banks in Indonesia,” Barekeng, vol. 19, no. 4, pp. 2467–2480, 2025, doi: 10.30598/barekengvol19iss4pp2467-2480.

I. Sriliana, I. N. Budiantara, and V. Ratnasari, “Poverty gap index modeling in Bengkulu Province using truncated spline regression for longitudinal data,” AIP Conf. Proc., vol. 2975, no. 1, 2023, doi: https://doi.org/10.1063/5.0181178.

World Health Organization, “Stunting in a Nutshell.” [Online]. Available: https://www.who.int/news/item/19-11-2015-stunting-in-a-nutshell

S. S. Anton, N. M. U. K. Dewi, and I. G. Adiba, “Kajian Determinan Stunting Pada Anak di Indonesia,” J. Yoga dan Kesehat., vol. 6, no. 2, pp. 201–217, 2023, doi: 10.25078/jyk.v6i2.2907.

D. A. Ningsih, “Kajian Determinan yang Berhubungan dengan Status Gizi Kurang pada Balita,” J. Ilmu Gizi Indones., vol. 3, no. 1, pp. 28–34, 2022, doi: 10.57084/jigzi.v3i1.885.




DOI: http://dx.doi.org/10.12962%2Fj27213862.v8i3.23330

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