Performance Quantile Regression and Bayesian Quantile Regression in Dealing with Non-normal Errors (Case Study on Simulated Data)

Authors

  • Lilis Harianti Hasibuan Universitas Islam Negeri Imam Bonjol Padang
  • Ferra Yanuar Universitas Andalas
  • Vika Pradinda Harahap Universitas Islam Negeri Imam Bonjol Padang
  • Latifatul Qalbi Universitas Islam Negeri Imam Bonjol Padang

DOI:

https://doi.org/10.25217/numerical.v8i2.4922

Keywords:

Gibbs Sampling, Mean Square Error (MSE), Quantile Regression, Normality Assumption

Abstract

This research discusses the performance of quantile regression and Bayesian quantile regression methods. Quantile regression uses parameter estimation by maximizing the value of the likelihood function, while Bayesian quantile regression uses parameter estimation with the Bayesian concept. The Bayesian concept in question looks for solutions from the posterior distribution with Gibbs Sampling. The purpose of the study is to compare the two methods. The data used is simulated data with a total of 100 generated data. The results obtained by the Bayesian quantile regression method are superior to the indicator used MSE with the result of 1.7445. The smallest MSE value is obtained in the model that is in quantile of 0.5

References

[1] L. Harianti Hasibuan, S. Musthofa, P. Studi Matematika, and U. Imam Bonjol Padang, “Journal of Science and Technology Penerapan Metode Regresi Linear Sederhana Untuk Prediksi Harga Beras di Kota Padang,” J. Sci. Technol., vol. 2, no. 1, pp. 85–95, 2022.

[2] L. H. Hasibuan, D. M. Putri, and M. Jannah, “Simple Linear Regression Method to Predict Cooking Oil Prices in the Time of Covid-19,” Logaritma J. Ilmu-ilmu Pendidik. dan Sains, vol. 10, no. 01, pp. 81–94, 2022.

[3] L. H. Hasibuan, D. M. Putri, M. Jannah, and S. Musthofa, “Analisis Metode Single Exponential Smoothing dan Metode Regresi Linear untuk Prediksi Harga Daging Ayam Ras” Math Educ. J., vol. 6, no. 2, pp. 120–130, 2022.

[4] A. S. Sholih, L. H. Hasibuan, and I. D. Rianjaya, “Analisis Regresi Logistik Ordinal terhadap Faktor-Faktor yang Mempengaruhi Predikat Kelulusan Mahasiswa Sarjana UIN Imam Bonjol Padang” MAp (Mathematics Appl. J., vol. 6, no. 2, pp. 99–110, 2024.

[5] L. H. Hasibuan, D. M. Putri, and M. Jannah, “Penerapan Metode Least Square Untuk Memprediksi Jumlah Penerimaan Mahasiswa Baru,” MAp (Mathematics Appl. J., vol. 4, no. 1, pp. 33–39, 2022.

[6] L. H. Hasibuan, F. Yanuar, D. Devianto, and M. Maiyastri, “Quantile Regression Analysis; Simulation Study With Violation of Normality Assumption,” JOSTECH J. Sci. Technol., vol. 4, no. 2, pp. 133–142, 2024.

[7] F. Yanuar, “The Simulation Study to Test the Performance of Quantile Regression Method With Heteroscedastic Error Variance,” Cauchy J. Mat. Murni dan Apl., vol. 5, no. 1, pp. 36–41, 2017.

[8] F. Yanuar, H. Yozza, and I. Rahmi, “Penerapan Metode Regresi Kuantil pada Kasus Pelanggaran Asumsi Kenormalan Sisaan,” Eksakta, vol. 1, pp. 33–37, 2016.

[9] F. Yanuar, A. S. Deva, A. Zetra, C. D. Yan, A. Rosalindari, and H. Yozza, “Bayesian regularized tobit quantile to construct stunting rate model,” Commun. Math. Biol. Neurosci., vol. 2023, p. Article-ID, 2023.

[10] L. H. Hasibuan, F. Yanuar, D. Devianto, M. Maiyastri, and A. Apriona, “Bayesian Method for Linear Regression Modeling; Simulation Study with Normality Assumption,” JOSTECH J. Sci. Technol., vol. 5, no. 1, pp. 81–92, 2025.

[11] K. Yu and R. A. Moyeed, “Bayesian quantile regression,” Stat. Probab. Lett., vol. 54, no. 4, pp. 437–447, 2001.

[12] R. Alhamzawi and K. Yu, “Variable selection in quantile regression via Gibbs sampling,” J. Appl. Stat., vol. 39, no. 4, pp. 799–813, 2012.

[13] D. F. Benoit, R. Alhamzawi, and K. Yu, “Bayesian lasso binary quantile regression,” Comput. Stat., vol. 28, pp. 2861–2873, 2013.

[14] R. Koenker and G. Bassett Jr, “Regression quantiles,” Econom. J. Econom. Soc., pp. 33–50, 1978.

[15] C. Davino, M. Furno, and D. Vistocco, Quantile regression: theory and applications, vol. 988. John Wiley & Sons, 2013.

[16] R. Koenker and K. F. Hallock, “Quantile regression,” J. Econ. Perspect., vol. 15, no. 4, pp. 143–156, 2001.

[17] L. J. Bain and M. Engelhardt, Introduction to Probability and Mathematical Statistics., vol. 49, no. 2. 1993. doi: 10.2307/2532587.

[18] F. Yanuar, H. Yozza, and R. V. Rescha, “Comparison of two priors in Bayesian estimation for parameter of Weibull distribution,” Sci. Technol. Indones., vol. 4, no. 3, pp. 82–87, 2019.

[19] R. J. T. Al-Hamzawi, “Prior elicitation and variable selection for bayesian quantile regression,” 2013, Brunel University, School of Information Systems, Computing and Mathematics.

[20] L. J. Bain and M. Engelhardt, Introduction to probability and mathematical statistics, vol. 4. Duxbury Press Belmont, CA, 1992.

[21] R. E. Walpole, R. H. Myers, S. L. Myers, and K. Ye, Probability and statistics for engineers and scientists, vol. 5. Macmillan New York, 1993.

[22] D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to linear regression analysis. John Wiley & Sons, 2021.

[23] R. Alhamzawi and H. T. M. Ali, “Brq: An R package for Bayesian quantile regression,” Metron, vol. 78, no. 3, pp. 313–328, 2020.

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Published

2024-12-30

How to Cite

Lilis Harianti Hasibuan, Ferra Yanuar, Harahap, V. P., & Qalbi, L. (2024). Performance Quantile Regression and Bayesian Quantile Regression in Dealing with Non-normal Errors (Case Study on Simulated Data). Numerical: Jurnal Matematika Dan Pendidikan Matematika, 8(2), 46–54. https://doi.org/10.25217/numerical.v8i2.4922

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Section

Artikel Pendidikan Matematika