A Sandwich Likelihood Correction for Bayesian Quantile Regression based on the Misspecified Asymmetric Laplace Density

TL;DR

This paper introduces a sandwich likelihood correction to improve Bayesian quantile regression when using the misspecified asymmetric Laplace density, enhancing inference accuracy while maintaining the approach's benefits.

Contribution

It proposes a novel sandwich likelihood correction method that addresses the limitations of Bayesian quantile regression with misspecified asymmetric Laplace models.

Findings

The correction improves inference accuracy in simulations.

Theoretical results support the validity of the approach.

Method maintains computational efficiency.

Abstract

A sandwich likelihood correction is proposed to remedy an inferential limitation of the Bayesian quantile regression approach based on the misspecified asymmetric Laplace density, by leveraging the benefits of the approach. Supporting theoretical results and simulations are presented.