A Combined Truncated Spline and Kernel Semiparametric Path Model Development

Usriatur Rohma, Adji Achmad Rinaldo Fernandes, Suci Astutik, Solimun Solimun

Abstract


Semiparametric path analysis is a combination of parametric and nonparametric path analysis performed when the linearity assumption in some relationships is not met. In this study, the development of semiparametric path function estimation was carried out by combining two truncated spline and kernel approaches. In addition, the purpose of this study is to determine the significance of function estimation using t-test statistics at the jackknife resampling stage. This research was conducted in 135 Junrejo sub-districts of Batu district.  The results showed that the development of a combined semiparametric path function estimation of truncated spline and kernel with weighted least square allows a more flexible and accurate estimation in modeling waste management behavior patterns. 2. The significance of the best truncated spline nonparametric path estimation in the model of the effect of Environmental Quality and the Use of Waste Banks on the Economic Benefits of Waste through the Use of the 3R Principles using t test statistics at the jackknife resampling stage shows that all exogenous variables have a significant effect on endogenous variables.

Keywords


Semiparametric Path Analysis; Truncated Spline; Kernel; Ramsey RESET; Economic Benefits of Waste

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References


[1] Solimun, Analisis Multivariat Pemodelan Struktural. Malang: CV Citra Malang, 2010.

[2] I. N. Budiantara, B. Lestari, and A. Islamiyati, “Weighted Partial Spline Estimators in Heteroscedastic Nonparametric and Semi-parametric Regression for Longitudinal Data,” 2009.

[3] A. A. R. Fernandes and Solimun, Analisis Regresi dalam Pendekatan Fleksibel. Malang: Universitas Brawijaya Press, 2021.

[4] P. D. Apriliyanti, “Waste Management Based on Community Empowerment in the Brantas River Watershed of Batu City,” 2024.

[5] D. Werdiono, “Seriously Tackling Waste at Tlekung Landfill in Batu City”.

[6] F. L. N. Rasyidah, “Estimasi Fungsi Jalur Nonparametrik Deret Fourier Dan Truncated Spline Pada Data Simulasi,” Brawijaya, 2022.

[7] R. L. Eubank, Nonparametric Regression and Spline Smoothing. CRC Press, 1999. doi: 10.1201/9781482273144.

[8] I. D. A. M. I. Wulandari and I. N. Budiantara, “Analysis of Factors Affecting the Percentage of Poor Population and Food Per Capita Expenditure in East Java using Birespon Spline Nonparametric Regression,” ITS Journal of Science and Arts, vol. 3, no. 1, pp. 30–35, 2014.

[9] H. Nurcahayani, I. N. Budiantara, and I. Zain, “The Curve Estimation of Combined Truncated Spline and Fourier Series Estimators for Multiresponse Nonparametric Regression,” Mathematics, vol. 9, no. 10, p. 1141, May 2021, doi: 10.3390/math9101141.

[10] A. A. R. Fernandes, I. N. Budiantara, B. W. Otok, and Suhartono, “Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data,” J Math Stat, vol. 11, no. 2, pp. 61–69, Feb. 2015, doi: 10.3844/jmssp.2015.61.69.

[11] C. Ho. Yu, “Resampling methods: concepts, applications, and justification,” Practical Assessment, Research & Evaluation, vol. 8, no. 19, pp. 1–23, 2003.

[12] I. Rodliyah, “Perbandingan Metode Bootstrap dan Jackknife dalam Mengestimasi Parameter Regresi Linier Berganda.,” JMPM: Jurnal Matematika dan Pendidikan Matematika, vol. I, no. 1, pp. 76–86, 2016.

[13] M. N. Aidi, “PERBAIKAN METODE KRIGING BIASA (ORDINARY KRIGING) MELALUI PEMECAHAN MATRIKS C MENJADI BEBERAPA ANAK MATRIKS NON OVERLAP UNTUK MEWAKILI DRIFT PADA PEUBAH SPASIAL,” Forum Statistika dan Komputasi, vol. 12, no. 1, 2007.




DOI: https://doi.org/10.18860/cauchy.v10i1.29849

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