Semiparametric Biresponse Regression Modeling Mixed Spline Truncated, Fourier Series, and Kernel in Predicting Rainfall and Sunshine
Keywords:
Biresponse Semiparametric Regression, Fourier Series, Generalized Cross Validation, Kernel, Spline Truncated
Abstract
The biresponse semiparametric regression analysis combines parametric and nonparametric components to understand the relationship between two correlated response variables and predictor variables. In this approach, the nonparametric component can be estimated using spline truncated, Fourier series, or kernel methods, each suitable for specific data patterns. This study aims to estimate the parameters of a mixed semiparametric regression model on climate data using the Weighted Least Square (WLS) method and to select optimal knot points, oscillation parameters, and bandwidth based on the smallest Generalized Cross Validation (GCV) value. The results show that the best model combines a spline truncated component with one knot and a Fourier series component with one oscillation, yielding a minimum GCV of 7.401, an R² of 84.66%, and an MSE of 92.33. The findings suggest that the biresponse semiparametric regression model combining spline truncated, Fourier series, and kernel estimators is highly effective for modeling climate data with complex predictor patterns.References
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Applied Data Sciences, vol. 5, no. 1, pp. 46–55, 2024. DOI: 10.47738/jads.v5i1.154.
[2] BMKG, “Informasi iklim bmkg untuk kenaikan suhu dan perkembangan iklim,” Tech. Rep., 2022. [Online].
Available: https://dataonline.bmkg.go.id/.
[3] D. Hafidz, A. Wardhana, and M. R. Prawira, “The analysis of indonesia’s climate change policies in response
to the 2021 intergovernmental panel on climate change (ipcc) assessment report / ar6 group 1 (2021-2023),”
Unknown Journal, vol. 1, pp. 42–53, 2023.
[4] T. Neya, G. Yanon, J. Soubeiga, R. Kiribou, O. Neya, and J. Magistro, “Climate change impact assessment
and disaster risk financing strategies in mali: A comprehensive analysis of drought and flood events,”
International Journal of Environment and Climate Change, vol. 14, no. 3, pp. 126–138, 2024. DOI: 10.
9734/ijecc/2024/v14i34025.
[5] Indonesian Agency for Meteorological Climatological and Geophysics, “Indonesia air quality annual report
2023,” Tech. Rep., 2023, pp. 1–28. [Online]. Available: https://iklim.bmkg.go.id/bmkgadmin/
storage/buletin/BMKG_20Climate_20Outlook_202023.pdf.
Stat., Optim. Inf. Comput. Vol. x, Month 202x
HARTINA HUSAIN ET.AL 13
[6] N. Ainun. “Banjir makassar meluas, warga mengungsi bertambah jadi 482 orang.” Retrieved March 29,
2024. (2023), [Online]. Available: https://www.detik.com/sulsel/berita/d-7147863/
banjir - makassar - meluas - warga - mengungsi - bertambah - jadi - 482 - orang# :˜:
text = Berdasarkan % 20data % 20Badan % 20Penanggulangan % 20Bencana , dan % 2017 %
20jiwa%20dari%20Biringkanaya.
[7] A. Yamin and J. Wiratmo, Klasifikasi wilayah rawan kekeringan pada lahan sawah non irigasi di sulawesi
selatan, 2020. [Online]. Available: https : / / www . researchgate . net / publication /
345387748 _ KLASIFIKASI _ WILAYAH _ RAWAN _ KEKERINGAN _ PADA _ LAHAN _ SAWAH _ NON _
IRIGASI_DI_SULAWESI_SELATAN.
[8] C. Zhang, Y. Zhang, J. Pu, Z. Liu, Z. Wang, and L. Wang, “An hourly solar radiation prediction model using
extreme gradient boosting algorithm with the effect of fog-haze,” Energy and Built Environment, Apr. 2023.
DOI: 10.1016/j.enbenv.2023.08.001.
[9] M. Ehteram and H. Shabanian, “Unveiling the salstm-m5t model and its python implementation for precise
solar radiation prediction,” Energy Reports, vol. 10, pp. 3402–3417, 2023. DOI: 10.1016/j.egyr.
2023.10.029.
[10] E. P. Prasetya and E. C. Djamal, “Rainfall forecasting for the natural disasters preparation using recurrent
neural networks,” in Proceedings of the International Conference on Electrical Engineering and Informatics,
2019, pp. 52–57. DOI: 10.1109/ICEEI47359.2019.8988838.
[11] M. Ramli, I. N. Budiantara, and V. Ratnasari, “A method for parameter hypothesis testing in nonparametric
regression with fourier series approach,” MethodsX, vol. 11, p. 102 468, 2023. DOI: 10.1016/j.mex.
2023.102468.
[12] L. Hidayati, N. Chamidah, and I. N. Budiantara, “Spline truncated estimator in multiresponse
semiparametric regression model for computer based national exam in west nusa tenggara,” IOP Conference
Series: Materials Science and Engineering, vol. 546, no. 5, p. 052 029, 2019. DOI: 10.1088/1757-
899X/546/5/052029.
[13] H. Husain, I. N. Budiantara, and I. Zain, “Mixed estimator of spline truncated, fourier series, and kernel in
biresponse semiparametric regression model,” IOP Conference Series: Earth and Environmental Science,
vol. 880, no. 1, p. 012 046, 2021. DOI: 10.1088/1755-1315/880/1/012046.
[14] B. Lestari, N. Chamidah, I. N. Budiantara, and D. Aydin, “Determining confidence interval and asymptotic
distribution for parameters of multiresponse semiparametric regression model using smoothing spline
estimator,” Journal of King Saud University - Science, vol. 35, no. 5, p. 102 664, 2023. DOI: 10.1016/j.
jksus.2023.102664.
[15] Hesikumalasari, I. N. Budiantara, and V. Ratnasari, “Pemodelan regresi semiparametrik menggunakan
estimator campuran spline truncated dan kernel,” Institut Teknologi Sepuluh Nopember, pp. 1–8, 2016.
[16] K. Nisa, “Model regresi semiparametrik campuran spline truncated dan deret fourier (studi kasus: Angka
harapan hidup provinsi jawa timur),” Unknown Journal, pp. 1–120, 2017.
[17] M. Fariz, F. Mardianto, P. Supervisor, N. Budiantara, and M. Si, “Semiparametric regression model of
biresponse using fourier series,” Unknown Journal, 2015.
[18] M. S. Sauri, M. Hadijati, and N. Fitriyani, “Spline and kernel mixed nonparametric regression for
malnourished children model in west nusa tenggara,” Jurnal Varian, vol. 4, no. 2, pp. 99–108, 2021. DOI:
10.30812/varian.v4i2.1003.
Published
2025-04-23
How to Cite
Husain, H., Rahayu, P. I., Nisardi, M. R., Al-Fadhilah, M. A., & Husain, A. (2025). Semiparametric Biresponse Regression Modeling Mixed Spline Truncated, Fourier Series, and Kernel in Predicting Rainfall and Sunshine. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2166
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Research Articles
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