A Simulation Study of Interval Estimation in Nonparametric Regression Using the Truncated Spline Estimator
DOI:
10.29303/jm.v7i3.9625Published:
2025-09-29Downloads
Abstract
This study examines interval estimation in truncated spline nonparametric regression using simulated data. The study aims to determine the impact of sample size, variance, and knot points on the performance of the truncated spline estimator. The results show that as the sample size increases, both the Generalized Maximum Likelihood (GML) and Mean Square Error (MSE) values decrease, while the coefficient of determination increases. This study also reveals that increasing the variance leads to higher GML and MSE values, as well as a lower coefficient of determination. Furthermore, the truncated spline nonparametric regression model achieves optimal performance with three knot points. The results showed that the more knot points, the GML and MSE values will decrease, while the coefficient of determination increases. The results of this study show that the determination of sample size, variance, and knot points significantly affects the accuracy and efficiency of the truncated spline nonparametric regression model, allowing it to serve as a reference for applying truncated spline nonparametric regression more effectively to produce a more optimal model that aligns with the characteristics of the data.
Keywords:
GML Interval Estimation Nonparametric Regression Simulation Study Spline TruncatedReferences
Adrianingsih, N. Y., Budiantara, I. N., & Purnomo, J. D. T. (2021). Modeling with Mixed Kernel, Spline Truncated and Fourier Series on Human Development Index in East Java. IOP Conf. Ser.: Mater. Sci. Eng., 1115(1), 1–9. https://doi.org/10.1088/1757-899x/1115/1/012024
Adrianingsih, N. Y., & Dani, A. T. R. (2021). Estimasi Model Regresi Semiparametrik Spline Truncated Menggunakan Metode Maximum Likelihood Estimation (MLE). Jambura Journal of Probability and Statistics, 2(2), 56–63. https://doi.org/10.34312/jjps.v2i2.10255
Adrianingsih, N. Y., Mungkabel, M., Dani, A. T. R., & Ni’matuzzahroh, L. (2025). A Nonparametric Regression Approach Address Poverty Problems in East Nusa Tenggara Province. Inferensi, 8(1), 67–74. https://doi.org/10.12962/j27213862.v8i1.20508
Dani, A. T. R., Adrianingsih, N. Y., Ainurrochmah, A., & Sriningsih, R. (2021). Flexibility of Nonparametric Regression Spline Truncated on Data without a Specific Pattern. Jurnal Litbang Edusaintech, 2(1), 37–43. https://doi.org/10.51402/jle.v2i1.30
Dani, A. T. R. D., Putra, F. B., Ni’matuzzahroh, L., Ratnasari, V., & Budiantara, I. N. (2024). BTS Buku Tentang Statistika Regresi Nonparametrik dan Non Parametrik Teori dan Aplikasi dengan Software R. Perkumpulan Rumah Cemerlang Indonesia.
Dani, A. T. R., Ni’matuzzahroh, L., Ratnasari, V., & Budiantara, I. N. (2021). Pemodelan Regresi Nonparametrik Spline Truncated pada Data Longitudinal (Studi Kasus: Persentase Penduduk Miskin Provinsi Papua Tahun 2016-2019). Inferensi, 4(1), 47–55. https://doi.org/10.12962/j27213862.v4i1.8737
Fitriyani, N., Hadijati, M., Harsyiah, L., & Sauri, M. S. (2021). Mixed Truncated Spline and Kernel Nonparametric Regression Model on Population Growth Rate in West Nusa Tenggara Province. IOP Conf. Ser.: Mater. Sci. Eng. 1115 012054, 1115(1), 1–8. https://doi.org/10.1088/1757-899x/1115/1/012054
Husain, H., Budiantara, I. N., & Zain, I. (2021). Mixed Estimator of Spline Truncated, Fourier Series, and Kernel in Biresponse Semiparametric Regression Model. IOP Conf. Ser.: Earth and Environ. Sci., 880(1), 1–11. https://doi.org/10.1088/1755-1315/880/1/012046
Islamiyati, A., Raupong, Kalondeng, A., & Sari, U. (2022). Estimating The Confidence Interval of The Regression Coefficient of The Blood Sugar Model Through a Multivariable Linear Spline with Known Variance. Statistics in Transition New Series (SiTns), 23(1), 201–212. https://doi.org/10.2478/stattrans-2022-0012
Kuswanto, H., Islamiyati, A., & Ilyas, N. (2022). Multilevel Nonparametric Regression Model with Truncated Linear Spline Estimator on Students’ National Examination Scores. International Journal of Academic and Applied Research (IJAAR), 6(2), 77–81. www.ijeais.org/ijaar
Ni’matuzzahroh, L., & Dani, A. T. R. (2024). Nonparametric Regression Modeling with Multivariable Fourier Series Estimator on Average Length of Schooling in Central Java in 2023. Inferensi, 7(2), 73–81. https://doi.org/10.12962/j27213862.v7i2.20219
Nurcahayani, H., Budiantara, I. N., & Zain, I. (2019). Nonparametric Truncated Spline Regression on Modelling Mean Years Schooling of Regencies in Java. AIP Conf. Proc., 2194, 1–8. https://doi.org/10.1063/1.5139805
Octavanny, M. A. D., Budiantara, I. N., Kuswanto, H., & Rahmawati, D. P. (2021). A New Mixed Estimator in Nonparametric Regression for Longitudinal Data. Journal of Mathematics, 2021, 1–12. https://doi.org/10.1155/2021/3909401
Prawanti, D. D., Budiantara, I. N., & Purnomo, J. D. T. (2019). Parameter Interval Estimation of Semiparametric Spline Truncated Regression Model for Longitudinal Data. IOP Conf. Ser.: Mater. Sci. Eng., 546(5), 1–10. https://doi.org/10.1088/1757-899X/546/5/052053
Ratnasari, V., Budiantara, I. N., & Dani, A. T. R. (2021). Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods. International Journal on Advanced Science Engineering Information Technology, 11(6), 2400–2406. https://doi.org/10.18517/ijaseit.11.6.14464
Setiawan, R. N. S., Budiantara, I. N., & Ratnasari, V. (2017). Application of Confidence Intervals for Parameters of Nonparametric Spline Truncated Regression on Index Development Gender in East Java. IPTEK, Journal of Science, 2(3), 49–55.
Setyawati, M., Chamidah, N., & Kurniawan, A. (2022). Confidence Interval of Parameters in Multiresponse Multipredictor Semiparametric Regression Model for Longitudinal Data Based on Truncated Spline Estimator. Commun. Math. Biol. Neurosci., 1–18. https://doi.org/10.28919/cmbn/7672
Sifriyani, Dani, A. T. R., Fauziyah, M., Hayati, M. N., Wahyuningsih, S., & Prangga, S. (2023). Spline and Kernel Mixed Estimators in Multivariable Nonparametric Regression for Dengue Hemorrhagic Fever Model. Commun. Math. Biol. Neurosci., 2023(11), 1–15. https://doi.org/10.28919/cmbn/7790
Sudiarsa, I. W. (2019). Simulations Study Combined Estimator Fourier Series and Spline Truncated in Multivariable Nonparametric Regression. IOP Conf. Ser.: Mater. Sci. Eng., 546(5), 1–10. https://doi.org/10.1088/1757-899X/546/5/052074
Suprapto. (2018). Interval Estimation for Indonesia Democracy Index (IDI) Model Using Multivariables Spline Truncated. International Journal of Scientific & Engineering Research, 9(9), 1740–1750. http://www.ijser.org
Wang, Y. (1998). Smoothing Spline Models with Correlated Random Errors. Journal of the American Statistical Association, 93(441), 341–348. https://doi.org/10.1080/01621459.1998.10474115
Widyastuti, D. A., Fernandes, A. A. R., & Pramoedyo, H. (2021). Spline Estimation Method in Nonparametric Regression using Truncated Spline Approach. J. Phys.: Conf. Ser., 1872(1), 1–9. https://doi.org/10.1088/1742-6596/1872/1/012027
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