Quantile Regression Analysis; Simulation Study With Violation of Normality Assumption

Lilis Harianti Hasibuan, Ferra Yanuar, Dodi Devianto, Maiyastri Maiyastri

Abstract


Quantile regression is an extension method of simple linear regression whose work is to separate or divide data into certain quantiles. This method minimizes the asymmetric absolute residual and estimates the conditional quantile function. Parameter estimation in the quantile regression method does not require the parametric assumption of normality. The data in this study are generated from different distributions. The distribution of the independent variables in this study comes from the t distribution, normal and exponential distribution. Meanwhile, the error distribution comes from the chi square distribution. This research produces various models of the selected quantiles. The estimated parameter values at each quantile are almost close to the initial values set. This research found the best model at quantile 0.5 by looking at the smallest MSE value of all quantiles of 1.2662. The best model obtained is .


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References


L. H. Hasibuan and S. Musthofa, “Penerapan Metode Regresi Linear Sederhana Untuk Prediksi Harga Beras di Kota Padang,” JOSTECH J. Sci. Technol., vol. 2, no. 1, pp. 85–95, 2022.

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

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

F. Yanuar, “Quantile Regression Approach to Determine the Indicator of Health Status,” Sci. Res. Journal, I, pp. 17–23, 2013.

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

F. Yanuar, L. Hasnah, and D. Devianto, “The Simulation Study to Test the Performance of Quantile Regression Method With Heteroscedastic Error Variance,” vol. 5, no. May, pp. 36–41, 2017.

R. Koenker, “Quantile regression for longitudinal data,” J. Multivar. Anal., vol. 91, no. 1, pp. 74–89, 2004.

H. Kozumi and G. Kobayashi, “Gibbs sampling methods for Bayesian quantile regression,” J. Stat. Comput. Simul., vol. 81, no. 11, pp. 1565–1578, 2011.

F. Yanuar, “The use of Uniformative and informative prior distribution in Bayesian SEM,” Glob. J. Pure Appl. Math., vol. 11, no. 5, pp. 3259–3264, 2015.

M. C. Korkmaz, E. Altun, C. Chesneau, and H. M. Yousof, “On the unit-Chen distribution with associated quantile regression and applications,” Math. Slovaca, vol. 72, no. 3, pp. 765–786, 2022.

F. Yanuar, C. Mukti, U. Andalas, and K. L. Manis, “Komparasi Model Pertambahan Tinggi Badan Balita Stunting Dengan Metode Regresi Kuantil dan Regresi Kuantil Bayesian,” vol. 20, no. 2, pp. 165–177, 2023.

Y. Wu and Y. Liu, “Variable selection in quantile regression,” Stat. Sin., pp. 801–817, 2009.

I. A. P. Uthami, I. K. G. Sukarsa, and I. P. E. Kencana, “Regresi Kuantil Median untuk Mengatasi Heteroskedastisitas pada Analisis Regresi,” E-Jurnal Mat., vol. 2, no. 1, pp. 6–13, 2013.

R. Koenker, V. Chernozhukov, X. He, and L. Peng, “Handbook of quantile regression,” 2017.

K. Yu, Z. Lu, and J. Stander, “Quantile regression: applications and current research areas,” J. R. Stat. Soc. Ser. D Stat., vol. 52, no. 3, pp. 331–350, 2003.

D. N. Gujarati, Essentials of econometrics. Sage Publications, 2021.

S. Bentzien and P. Friederichs, “Decomposition and graphical portrayal of the quantile score,” Q. J. R. Meteorol. Soc., vol. 140, no. 683, pp. 1924–1934, 2014.




DOI: https://doi.org/10.15548/jostech.v4i2.9643

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