### Simulation Study The Using of Bayesian Quantile Regression in Nonnormal Error

Catrin Muharisa, Ferra Yanuar, Dodi Devianto

#### Abstract

The purposes of this paper is  to introduce the ability of the Bayesian quantile regression method in overcoming the problem of the nonnormal errors using asymmetric laplace distribution on simulation study. Method: We generate data and set distribution of error is asymmetric laplace distribution error, which is non normal data.  In this research, we solve the nonnormal problem using quantile regression method and Bayesian quantile regression method and then we compare. The approach of the quantile regression is to separate or divide the data into any quantiles, estimate the conditional quantile function and minimize absolute error that is asymmetrical. Bayesian regression method used the asymmetric laplace distribution in likelihood function. Markov Chain Monte Carlo method using Gibbs sampling algorithm is applied then to estimate the parameter in Bayesian regression method. Convergency and confidence interval of parameter estimated are also checked. Result: Bayesian quantile regression method results has more significance parameter and smaller confidence interval than quantile regression method. Conclusion: This study proves that Bayesian quantile regression method can produce acceptable parameter estimate for nonnormal error.

#### Keywords

Quantile regression; Asymmetric laplace distribution; Gibbs sampling; Markov Chain Monte Carlo; Bayesian quantile regression

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#### References

Benoit, D.F and Van den Poel, D. 2017. BayesQR: A Bayesian Approach to Quantile Regression.Journal of Statistical Software, 76(7), 1-32.

Box, G.E.P and Tiao, G.C. 1973. Bayesian Inference In Statistical Analysis. AddisionWesley Company. Inc : Philippines.

Davino, C., Furno, M. and Vistocco, D. 2014. Quantile Regression Theory and Applications. John Wiley and Sons, Ltd.

Koenkar,R and Basset,G.Jr. 1978. Regression Quantiles. Econometrica,46: 33-50

Ntzoufras, I. 2009. Bayesian Modeling Using WINBugs. John Wiley Sons, Inc: New Jersey.

Walpole, R.E and Myers, R. H. 1995. Ilmu Peluang dan Statistika untuk Insinyur dan Ilmuwan Edisi ke-4. ITB : Bandung.

Yang, Y., Wang, H.J., He, X. 2015. Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood. International Statistical Review, 84(3), 327344.

Yu, K. 2003. Quantile regression: Aplications and Current Research Area. The Statistician, 52 (3): 331-350.

Yu, K. and Moyeed, R. 2001. Bayesian Quantile Regression. Statistics & Probability Letters, 54(4), 437-447.

Yu, K., and Zhang, J. 2005. A three-parameter asymmetric Laplace distribution and its extension. Communications in Statistics-Theory and Methods, 34(9-10), 1867-1879.

DOI: https://doi.org/10.18860/ca.v5i3.5633

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