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 pr...

This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distributi...

Bayesian quantile regression has drawn more attention in widespread applications recently. Yu and Moyeed (2001) proposed an asymmetric Laplace distribution to provide likelihood based mechanism for Bayesian inference of quantile regression models. In this work, the primary objective is to evaluate the performance of Bayesian quantile regression compared with simple regression and quantile regre...

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower tails. This paper develops a theory of quantile regression in the tails. Specifically , it obtains the large sample properties of extremal (ext...

[To be revised.] Quantile and expectile regression are tail oriented conditional regression. They can be transformed as generalized quantile regression. Traditional generalized quantile regression focuses on a single curve. When more random curves are available, we can estimate the single curves jointly by using the information from all subjects instead of estimate it individually. To avoid too...