Hartina Husain
Data Science Study Program, Institut Teknologi Bacharuddin Jusuf Habibie

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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
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33543

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.
Combined Truncated Spline and Fourier series in Nonparametric Biresponse Regression: A Case of Agricultural Productivity Hartina Husain; Rizki Aristyarini; Andi Oxy Raihan Machikami Rahman; Nur Rahmi; Muhammad Rifki Nisardi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.35319

Abstract

Agriculture plays a strategic role in supporting economic development and food security in Indonesia, particularly in South Sulawesi, one of the country’s primary rice-producing regions. Existing studies on agricultural productivity commonly rely on parametric or single-response models, which are less effective in capturing the nonlinear, locally varying, and interrelated characteristics of agricultural indicators. Addressing this research gap, the present study applies a biresponse nonparametric regression approach that integrates truncated splines and Fourier series to simultaneously model rice productivity and the food security index. This quantitative observational research uses secondary regional agricultural statistics, and the analytical procedure includes formulating the biresponse model, conducting diagnostic checks of key nonparametric assumptions, and estimating parameters using the Weighted Least Squares (WLS) method. Model selection was conducted using the Generalized Cross Validation (GCV) criterion, which indicated that rainfall was better approximated with truncated splines and extension workers with Fourier series. The optimal knot points were obtained at 1207.096 for rice productivity variable and 1207.556 for food security index variable, with one oscillation applied in the Fourier series and one knot for the truncated spline. The results show that the best model was obtained with the smallest Generalized Cross Validation (GCV) value of 21.38, a coefficient of determination of 94.85%, and a Mean Absolute Percentage Error (MAPE) of 9.68%. These results demonstrate the methodological advantage of the combined biresponse nonparametric model in accommodating complex data structures and provide actionable insights for policymakers in optimizing resource allocation, strengthening extension services, and enhancing food security strategies in South Sulawesi.