Penerapan Keluarga Model Spline Truncated Polinomial pada Regresi Nonparametrik

Andrea Tri Rian Dani, Ludia Ni’matuzzahroh


One approach that is often used by researchers to determine the form of the relationship pattern between the response variables and predictor variables in regression analysis, namely the nonparametric approach, where the approach is used when the shape of the regression curve is assumed to be unknown. The truncated spline is a polynomial model in nonparametric regression that has segmented properties, where these properties provide better flexibility than ordinary polynomial models and are able to handle data whose behavior changes in certain sub-intervals due to the knot points in it. This study aims to apply a family of spline truncated polynomial models to nonparametric regression in the case of automotive data. The estimation method used is Ordinary Least Square (OLS). The number of knot points tested is 1 to 4-knot points with a degree of p=1,2,3. Based on the results of the analysis, the best model that produces the smallest GCV value is the nonparametric spline truncated quadratic regression model with 4 knots, which produces a GCV value of 522.27 and a coefficient of determination of 79.77%.


GCV; Nonparametric Regression; Polynomial Truncated Spline

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Berkarakter,”Prosiding Seminar Nasional FMIPA Undhiksa, pp. 09–28, 2011.

I. N. Budiantara, “Model Keluarga Spline Polinomial Truncated dalam Regresi Semiparametrik,”Berkala MIPA, vol. 15(3), pp. 55–61, 2005.

R. L. Eubank, Nonparametric Regression and Spline Smoothing. New York: Marcel Dekker, 1999.

W. Hardle, Applied Nonparametric Regression. New York: Cambridge University Press, 1990.

E. Montoya, N. Ulloa, dan V. Miller, “A Simulation Study Comparing Knot Slection Methods with Equally Spaced Knots in a Penalized Regression Spline,”International Journal of Statistics and Probability, vol. 03(03), pp. 96–110, 2014.

I. N. Budiantara, Regresi Nonparametrik Spline Truncated. Surabaya: ITS Press, 2019.

A. Tripena, “Analisis Regresi Spline Kuadratik,” dipresentasikan dalam Seminar Nasional Matematika dan Pendidikan Matematika, Jurusan Pendidikan Matematika, FMIPA UNY, 2011.

I. N. Budiantara, M. Ratna, I. Zain, dan W. Wibowo, “Modeling the Percentage of Poor People in Indonesia Using Spline Nonparametric Regression Approach,”International Journal of Basic & Applied Sciences IJBAS-IJENS, vol. 12, no. 06, pp. 119–124, 2012.

R. K. Dewi dan I. N. Budiantara “Faktor-Faktor yang Mempengaruhi Angka Gizi Buruk di Jawa Timur dengan Pendekatan Regresi Nonparametrik Spline,”JURNAL SAINS DAN SENI ITS, vol. 1, no. 1, pp. D177–D182, 2012.

M. F. Bintariningrum dan I. N. Budiantara “Pemodelan Regresi Nonparametrik Spline Truncated dan Aplikasinya pada Angka Kelahiran Kasar di Surabaya,”JURNAL SAINS DAN SENI POMITS, vol. 3, no. 1, pp. D-7–D-12, 2014.

N. Arfan dan I. N. Budiantara, “Pendekatan Spline untuk Estimasi Kurva Regresi Nonparametrik (Studi Kasus pada Data Angka Kematian Maternal di Jawa Timur),”JURNAL SAINS DAN SENI POMITS, vol. 3, no. 1, pp. D-13–D-17, 2014.

A. Islamiyati,“Spline Polynomial Truncated dalam Regresi Nonparametrik,”Jurnal Matematika, Statistika, & Komputasi, vol. 14, no. 1, pp. 54–60, 2017.

D. R. S. Saputro, K. R. Demu, dan P. Widyaningsih, “Nonparametric Truncated Spline Regression Model on Data of Human Development Index (HDI) in Indonesia,”IOP Conf. Series: Journal of Physics, vol. 1188, pp. 01–01, 2018.

A. T. R. Dani, N. Y. Adrianingsih, dan A. Ainurrochmah, “Pengujian Hipotesis Simultan Model Regresi Nonparametrik Spline Truncated dalam Pemodelan Kasus Ekonomi,”JAMBURA Journal of Probability and Statistics, vol. 01, pp. 98–106, 2020.

A. T. R. Dani, N. Y. Adrianingsih, A. Ainurrochmah, dan R. Sriningsih, “Flexibility of Nonparametric Regression Spline Truncated on Data without a Specific Pattern,”Jurnal Litbang Edusaintech, vol. 2(1), pp. 37–43, 2021.

A. T. R. Dani, L. Ni’matuzzahroh, V. Ratnasari, dan I. N. Budiantara, “Pemodelan Regresi Nonparametrik Spline Truncated pada Data Longitudinal,”INFERENSI, vol. 4(1), pp. 47–55, 2021.

A. T. R. Dani dan L. Ni’matuzzahroh, “Pemodelan Persentase Penduduk Miskin Kabupaten/Kota di Provinsi Jawa Barat dengan Pendekatan Regresi Nonparametrik Spline Truncated,”J Statistika, vol. 14, no. 1, pp. 24–29, 2021.

W. Hardle, Applied Nonparametric Regression. Berlin: Humboldt-Universitat zu Berlin, 1994.

G. Wahba, Spline Models for Observational Data. Pennsylvania: SIAM, 1990.

A. T. R. Dani, V. Ratnasari, and I. N. Budiantara, “Optimal Knots Point and Bandwidth Selection in Modeling Mixed Estimator Nonparametric Regression,” IOP Conf. Ser. Mater. Sci. Eng., vol. 1115, no. 1, p. 012020, 2021, doi: 10.1088/1757-899x/1115/1/012020.

V. Ratnasari, I. N. Budiantara, and A. T. R. Dani, “Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation ( CV ), Generalized Cross- Validation ( GCV ), and Unbiased Risk ( UBR ) Methods,” Int. J. Adv. Sci. Eng. Inf. Technol., vol. 11, no. 6, pp. 2400–2406, 2021.



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