Bayesian weighted composite quantile regression estimation for linear regression models with autoregressive errors

Abstract

Composite quantile regression methods have been shown to be effective techniques in improving the prediction accuracy. In this article, we propose a Bayesian weighted composite quantile regression estimation procedure to estimate unknown regression coefficients and autoregressive parameters in the linear regression models with autoregressive errors. A Bayesian joint hierarchical model is established using the working likelihood of the asymmetric Laplace distribution. Adaptive Lasso-penalized type priors are used on regression coefficients and autoregressive parameters of the model to conduct inference and variable selection simultaneously. A Gibbs sampling algorithm is developed to simulate the parameters from the posterior distributions. The proposed method is illustrated by some simulation studies and analyzing a real data set. Both simulation studies and real data analysis indicate that the proposed approach performs well.

Keywords:

• Autoregressive error
• composite quantile regression
• joint hierarchical model
• linear regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62J05
• 62J07
• 62G08

Notes

1 None of the regression coefficients and autoregressive parameters in the model are equal to zero.

2 Several regression coefficients and autoregressive parameters in the model are exactly equal to zero.