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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Muharisa, Catrin
Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang
Mathematics

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Simulation Study The Using of Bayesian Quantile Regression in Nonnormal Error Muharisa, Catrin; Yanuar, Ferra; Devianto, Dodi
CAUCHY Vol 5, No 3 (2018): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (557.993 KB) | DOI: 10.18860/ca.v5i3.5633

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.
Co-Authors Devianto, Dodi Yanuar, Ferra