Bayesian quantile regression with the asymmetric Laplace distribution

2020 ◽  
pp. 1-25
Author(s):  
J.-L. Dortet-Bernadet ◽  
Y. Fan ◽  
T. Rodrigues
Keyword(s):  
Quantile Regression ◽  
Laplace Distribution ◽  
Asymmetric Laplace Distribution ◽  
Bayesian Quantile Regression

scholarly journals Simulation Study The Using of Bayesian Quantile Regression in Nonnormal Error

CAUCHY ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. 121
Author(s):  
Catrin Muharisa ◽  
Ferra Yanuar ◽  
Dodi Devianto
Keyword(s):  
Confidence Interval ◽  
Quantile Regression ◽  
Simulation Study ◽  
Likelihood Function ◽  
Laplace Distribution ◽  
Regression Method ◽  
Bayesian Regression ◽  
Asymmetric Laplace Distribution ◽  
Bayesian Quantile Regression ◽  
Quantile Regression Method

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.

scholarly journals Power Prior Elicitation in Bayesian Quantile Regression

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Rahim Alhamzawi ◽  
Keming Yu
Keyword(s):  
Quantile Regression ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Real Data ◽  
Laplace Distribution ◽  
Scale Mixture ◽  
Prior Elicitation ◽  
Bayesian Quantile Regression ◽  
Critical Issues ◽  
Power Prior

We address a quantile dependent prior for Bayesian quantile regression. We extend the idea of the power prior distribution in Bayesian quantile regression by employing the likelihood function that is based on a location-scale mixture representation of the asymmetric Laplace distribution. The propriety of the power prior is one of the critical issues in Bayesian analysis. Thus, we discuss the propriety of the power prior in Bayesian quantile regression. The methods are illustrated with both simulation and real data.

scholarly journals Quantile regression for longitudinal data via the multivariate generalized hyperbolic distribution

2021 ◽  
pp. 1471082X2110154
Author(s):  
Alvaro J. Flórez ◽  
Ingrid Van Keilegom ◽  
Geert Molenberghs ◽  
Anneleen Verhasselt
Keyword(s):  
Quantile Regression ◽  
Growth Curves ◽  
Likelihood Estimation ◽  
Laplace Distribution ◽  
Generalized Hyperbolic Distribution ◽  
Asymmetric Laplace Distribution ◽  
Potential Applications ◽  
Joint Examination ◽  
Limiting Case ◽  
Theoretical Considerations

While extensive research has been devoted to univariate quantile regression, this is considerably less the case for the multivariate (longitudinal) version, even though there are many potential applications, such as the joint examination of growth curves for two or more growth characteristics, such as body weight and length in infants. Quantile functions are easier to interpret for a population of curves than mean functions. While the connection between multivariate quantiles and the multivariate asymmetric Laplace distribution is known, it is less well known that its use for maximum likelihood estimation poses mathematical as well as computational challenges. Therefore, we study a broader family of multivariate generalized hyperbolic distributions, of which the multivariate asymmetric Laplace distribution is a limiting case. We offer an asymptotic treatment. Simulations and a data example supplement the modelling and theoretical considerations.

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