Estimasi Produksi Beras dengan Estimator Campuran Spline Truncated – Kernel di Jawa Timur

Andrea Tri Rian Dani, Fachrian Bimantoro Putra, I Nyoman Budiantara, Vita Ratnasari

Abstract


This study aims to apply a nonparametric regression model using a mixed estimator of Truncated Spline and Kernel to estimate Rice Production in East Java Province. This model combines several predictor variables, namely Harvested Area of Rice Plants, Rice Productivity, Population, and Human Development Index. The selection of the best combination of variables is based on the lowest Generalized Cross-Validation (GCV) value to obtain a stable and accurate model. The results show that the model with a combination of variables Harvested Area of Rice Plants and Rice Productivity set as Truncated Spline components with three knot points, and Population and Human Development Index as Kernel components produces a minimum GCV value of 85,504,949, RMSE of 242,723.6, and R² of 91.24%. This model successfully captures non-linear relationship patterns and provides more stable estimates. The implication of this finding is that the resulting model can be used to design more efficient agricultural policies, by considering the factors that interact dynamically in rice production.

Keywords


Mixed Estimators; Truncated Spline-Kernel; GCV; Rice Production; Nonparametric Regression

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References


X. Zhang, J. Ru, and C. Wu, “A Nonparametric Regression-Based Multi-Scale Gradient Correlation Filtering Method for Infrared Small Target Detection,” Electronics (Switzerland), vol. 12, no. 7, Apr. 2023, doi: 10.3390/electronics12071562.

V. Ratnasari, S. H. Utama, and A. T. R. Dani, “Toward Sustainable Development Goals (SDGs) with Statistical Modeling: Recursive Bivariate Binary Probit,” IAENG International Journal of Applied Mathematics, vol. 54, no. 8, pp. 1515–1521, 2024.

I. N. Budiantara et al., “Modeling Percentage of Poor People in Indonesia Using Kernel and Fourier Series Mixed Estimator in Nonparametric Regression,” Revista Investigacion Operacional, vol. 40, no. 4, pp. 538–550, 2019.

P. Čížek and S. Sadıkoğlu, “Robust nonparametric regression: A review,” Wiley Interdiscip Rev Comput Stat, vol. 12, no. 3, pp. 1–16, May 2020, doi: 10.1002/wics.1492.

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, Mar. 2021, doi: 10.1088/1757-899x/1115/1/012020.

V. Ratnasari, Purhadi, I. C. Aviantholib, and A. T. R. Dani, “Parameter Estimation and Hypothesis Testing The Second Order of Bivariate Binary Logistic Regression (S-BBLR) Model With Berndt Hall-Hall-Hausman (BHHH) Iterations,” Communications in Mathematical Biology and Neuroscience, vol. 2022, 2022, doi: 10.28919/cmbn/7258.

E. A. Souza-Rodrigues, “Nonparametric regression with common shocks,” Econometrics, vol. 4, no. 3, Sep. 2016, doi: 10.3390/econometrics4030036.

L. R. Cheruiyot, “Local linear regression estimator on the boundary correction in nonparametric regression estimation,” Journal of Statistical Theory and Applications, vol. 19, no. 3, pp. 460–471, Sep. 2020, doi: 10.2991/jsta.d.201016.001.

E. Seijo and B. Sen, “Nonparametric least squares estimation of a multivariate convex regression function,” Ann Stat, vol. 39, no. 3, pp. 1633–1657, 2011, doi: 10.1214/10-AOS852.

S. Sifriyani, A. T. R. Dani, M. Fauziyah, M. N. Hayati, S. Wahyuningsih, and S. Prangga, “Spline and Kernel Mixed Estimators In Multivariable Nonparametric Regression For Dengue Hemorrhagic Fever Model,” Commun. Math. Biol. Neurosci., vol. 2023, pp. 1–15, 2023.

S. Sifriyani, A. T. R. Dani, M. Fauziyah, and I. N. Budiantara, “Statistical Modeling: A New Regression Curve Approximation using Mixed Estimators Truncated Spline and Epanechnikov Kernel,” Engineering Letters, vol. 31, no. 4, pp. 1–7, 2023.

R. Rahmania, S. Sifriyani, and A. T. R. Dani, “Modeling Open Unemployment Rate in Kalimantan Island Using Nonparametric Regression With Fourier Series Estimator,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 18, no. 1, pp. 0245–0254, Mar. 2024, doi: 10.30598/barekengvol18iss1pp0245-0254.

M. Rifada, N. Chamidah, R. A. Ningrum, and L. Muniroh, “Stunting Determinants Among Toddlers in Probolinggo District of Indonesia Using Parametric and Nonparametric Ordinal Logistic Regression Models,” Communications in Mathematical Biology and Neuroscience, vol. 2023, 2023, doi: 10.28919/cmbn/6690.

I. N. Budiantara, V. Ratnasari, M. Ratna, and I. Zain, “The Combination of Spline and Kernel Estimator for Nonparametric Regression and its Properties,” Applied Mathematical Sciences, vol. 9, no. 122, pp. 6083–6094, 2015, doi: 10.12988/ams.2015.58517.

I. Wayan Sudiarsa, I. Nyoman Budiantara, S. Suhartono, and S. W. Purnami, “Combined estimator fourier series and spline truncated in multivariable nonparametric regression,” Applied Mathematical Sciences, vol. 9, no. 97–100, pp. 4997–5010, 2015, doi: 10.12988/ams.2015.55394.

V. Ratnasari, N. Budiantara, M. Ratna, and I. Zain, “Estimation of Nonparametric Regression Curve using Mixed Estimator of Multivariable Truncated Spline and Multivariable Kernel,” Global Journal of Pure and Applied Mathematics, vol. 12, no. 6, pp. 5047–5057, 2016, [Online]. Available: http://www.ripublication.com/gjpam.htm

N. Chamidah, B. Lestari, I. N. Budiantara, and D. Aydin, “Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator,” Symmetry (Basel), vol. 16, no. 4, pp. 1–25, Apr. 2024, doi: 10.3390/sym16040386.

M. A. D. Octavanny, I. N. Budiantara, H. Kuswanto, and D. P. Rahmawati, “A New Mixed Estimator in Nonparametric Regression for Longitudinal Data,” Journal of Mathematics, vol. 2021, 2021, doi: 10.1155/2021/3909401.

D. P. Rahmawati, I. N. Budiantara, D. D. Prastyo, and M. A. D. Octavanny, “Mixed Spline Smoothing and Kernel Estimator in Biresponse Nonparametric Regression,” Int J Math Math Sci, vol. 2021, 2021, doi: 10.1155/2021/6611084.

N. P. A. M. Mariati, I. N. Budiantara, and V. Ratnasari, “The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression,” Symmetry (Basel), vol. 13, no. 11, Nov. 2021, doi: 10.3390/sym13112094.

V. Ratnasari, 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,” International Journal on Advanced Science Engineering Information Technology, vol. 11, no. 6, pp. 2400–2406, 2021.

H. Husain, I. N. Budiantara, and I. Zain, “Mixed estimator of spline truncated, Fourier series, and kernel in biresponse semiparametric regression model,” in IOP Conference Series: Earth and Environmental Science, IOP Publishing Ltd, Nov. 2021. doi: 10.1088/1755-1315/880/1/012046.

A. T. R. Dani, L. Ni’matuzzahroh, V. Ratnasari, and I. N. Budiantara, “Pemodelan Regresi Nonparametrik Spline Truncated pada Data Longitudinal,” Inferensi, vol. 4, no. 1, p. 47, Mar. 2021, doi: 10.12962/j27213862.v4i1.8737.

M. D. Regier and R. D. Parker, “Smoothing using fractional polynomials: An alternative to polynomials and splines in applied research,” Wiley Interdiscip Rev Comput Stat, vol. 7, no. 4, pp. 275–283, Jul. 2015, doi: 10.1002/wics.1355.

L. N. Berry and N. E. Helwig, “Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines,” Stats (Basel), vol. 4, no. 3, pp. 701–724, Sep. 2021, doi: 10.3390/stats4030042.

N. Y. Adrianingsih, I. N. Budiantara, and J. D. T. Purnomo, “Modeling with Mixed Kernel, Spline Truncated and Fourier Series on Human Development Index in East Java,” IOP Conf Ser Mater Sci Eng, vol. 1115, no. 1, p. 012024, Mar. 2021, doi: 10.1088/1757-899x/1115/1/012024.

W. Cui and M. Wei, “Strong Consistency of Kernel Regression Estimate,” Open J Stat, vol. 03, no. 03, pp. 179–182, 2013, doi: 10.4236/ojs.2013.33020.




DOI: https://doi.org/10.37905/jjom.v7i2.33379



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