An Adaptable Bayesian Quantile‐Based Regression Framework for Asymmetric Data Structures and Extreme Points

What the paper says

Quantile regression has attracted considerable attention due to allowing more comprehensive information on various features of the response distribution. In quantile‐based total regression modeling, novel flexible distributions are frequently requested. This paper introduces a convenient technique that utilizes an asymmetric exponential power distribution to address several features of quantile‐based regression models. Primary advantages include its ability to handle asymmetric data structures and extreme quantiles efficiently. It also improves robustness towards outlying data points, reducing their impact on the general analysis. Controlling the decay of both left and right tails provides a balanced illustration of the response distribution and enables a flexible estimation of the covariate's impact on response quantiles. The model encompasses several commonly used quantile‐based regressions and the traditional asymmetric Laplace. The study employs the Metropolis‐within‐Gibbs sampling algorithm to perform Bayesian inference and facilitate the quantile estimate. The model's performance is evaluated through simulation studies and empirical results. Notably, the model outperforms the asymmetric Laplace quantile regression in accurately capturing extreme quantile levels. These findings emphasize the practicality of our methodology in fitting quantile regression.