Parameter: Jurnal Matematika, Statistika dan Terapannya
Vol 5 No 1 (2026): Parameter: Jurnal Matematika, Statistika dan Terapannya

Parameter Estimation of Partial Spline Regression Using Weighted Least Squares with Moving Average Approach

Jiran Julita (Institut Teknologi Sepuluh Nopember, Indonesia)
Jerry Dwi Trijoyo Purnomo (Institut Teknologi Sepuluh Nopember, Indonesia)
I Nyoman Budiantara (Institut Teknologi Sepuluh Nopember, Indonesia)



Article Info

Publish Date
01 Jun 2026

Abstract

Regression analysis is a statistical method used to model the relationship between predictor variables and a response variable. In analyzing stunting prevalence, conventional parametric approaches are often limited in capturing complex and nonlinear patterns in the data. Therefore, a semiparametric regression approach is used, as it combines parametric and nonparametric components, providing greater flexibility in modeling relationships between variables. The truncated spline method is applied to accommodate nonlinear patterns, particularly in the variable of access to proper sanitation. This study aims to model the prevalence of stunting in Indonesia using a truncated spline semiparametric regression approach, with the percentage of poor population as the parametric component and access to proper sanitation as the nonparametric component. Parameter estimation is conducted using Ordinary Least Squares (OLS) and improved using Weighted Least Squares (WLS) with a moving average approach to address heteroscedasticity. The optimal model is selected based on the minimum Generalized Cross Validation (GCV) value. The results show that the best model is obtained with order 1 and one knot point at 93.884, producing the minimum GCV value of 25.19599. The WLS approach improves the model performance, increasing the coefficient of determination (R²) from 53.25% to 74.40%, and successfully overcomes heteroscedasticity issues. The analysis also indicates that the percentage of poor population has a positive effect on stunting prevalence, while access to proper sanitation has a negative and nonlinear effect, with a stronger impact after exceeding the knot point. These findings indicate that the truncated spline semiparametric regression model with WLS estimation provides a better and more reliable approach in modeling stunting prevalence.

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Journal Info

Abbrev

parameter

Publisher

Subject

Mathematics

Description

Parameter: Jurnal Matematika, Statistika dan Terapannya is an open access journal (e-journal) published since April 2022. Parameteris published by Department of Mathematics, Faculty of Science and Mathematics, Pattimura. Parameterpublished scientific articles on various aspects related to ...