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All Journal Journal of Mathematics, Computation and Statistics (JMATHCOS)
Jiran Julita
Institut Teknologi Sepuluh November
Mathematics

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Semiparametric Spline Regression with Moving Average Smoothing Under Heteroscedastic Errors for Childhood Stunting Prevalence in Indonesia Jiran Julita; Jerry Dwi Trijoyo Purnomo; I Nyoman Budiantara
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/cgmfwz19

Abstract

Stunting prevalence remains a critical public health issue in Indonesia due to its long-term impact on child development and human capital. This study aims to model stunting prevalence using a semiparametric regression approach with truncated spline functions, which allows for capturing both linear and nonlinear relationships between variables. The percentage of poor population is treated as the parametric component, while immunization coverage is modeled as the nonparametric component. Model estimation is initially performed using Ordinary Least Squares, where the best model is obtained with two knot points and a minimum Generalized Cross Validation value of 21.74771. However, residual diagnostics indicate the presence of heteroscedasticity. To address this issue, Weighted Least Squares with a moving average approach is applied. The results show that the optimal weighted model uses three knot points with a cubic spline, producing a lower GCV value of 14.48820 and a higher coefficient of determination of 86.78 percent compared to 61.98 percent in the OLS model. Furthermore, all residual assumptions are satisfied under the weighted approach. These findings indicate that the WLS method with moving average provides a more accurate, stable, and reliable model for analyzing stunting prevalence.  
Co-Authors I Nyoman Budiantara Jerry Dwi Trijoyo Purnomo