Simulation Study The Using of Bayesian Quantile Regression in Nonnormal Error

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. <strong>Method: </strong>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. <strong>Result: </strong>Bayesian quantile regression method results has more significance parameter and smaller confidence interval than quantile regression method. <strong>Conclusion: </strong>This study proves that Bayesian quantile regression method can produce acceptable parameter estimate for nonnormal error.

Identification of Rainfall Distribution in West Sumatera and Assessment of Its Parameters Using Bayes Method

“…In this research, the distribution of the average rainfall data and its parameter estimation will be determined using direct estimation (maximum likelihood estimator or MLE) and indirect estimation (Bayes method) (Badjana et al, 2017;Heaps et al, 2015;Yosboonruang et al, 2019). In the Bayes method, the model parameters to be estimated are assumed to be random variables that have a certain distribution, which is stated as the prior distribution, while the information regarding the probability density function is expressed in the form of the likelihood function (Aini et al, 2019;Muharisa et al, 2018;Yanuar et al, 2019). The model parameter with Bayes is estimated by determining the posterior distribution which is obtained proportionally from the likelihood distribution and the prior distribution.…”

Simulation Study of Autocorrelated Error Using Bayesian Quantile Regression

“…In previous studies (Muharisa et al, 2018), the Bayesian Quantile Regression Method with Abnormal Error has been discussed in the case of Low Birth Weight (BBLR) in West Sumatra in the data of 2016 to 2018. Furthermore (Delviyanti et al, 2018) has been examined the application of the Quantile Regression with the Bootstrap Method to the autocorrelated error in the case of the interest rate on Indonesia's in ation rate.…”

Applying bootstrap quantile regression for the construction of a low birth weight model

“…However, studies have shown that the resulting estimates of various effects on the conditional mean of birth weight do not necessarily indicate the size and nature of these effects on the lower tail of the birth weight distribution. 4,5 A more complete picture of the covariate effects can be seen by estimating a family of conditional quantile functions. Estimates of conditional quantiles can be used overcome any problem associated with the classical method (OLS), such as outlier data or heteroscedasticity cases, as long as the error distribution of the data has a continuous, symmetric, and unimodal density.…”