In several regression applications, a different structural relationship might be anticipated for the higher or lower responses than the average responses. In such cases, quantile regression analysis can uncover important features that would likely be overlooked by traditional mean regression. We develop a Bayesian method for fully nonparametric model-based quantile regression. The approach invo...

Quantile regression is an increasingly important tool that estimates the conditional quantiles of a response Y given a vector of regressors D. It usefully generalizes Laplace’s median regression and 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. For the linear quantile model defined by Y = D′γ(U) where D′γ(U) is s...

We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial quantile regression (PQR) basis for estimating functional coefficients. We further extend our partial quantile covariance techniques to functional composite quantil...

Quantile regression as an alternative to conditional mean regression (i.e., least square regression) is widely used in many areas. It can be used to study the covariate effects on the entire response distribution by fitting quantile regression models at multiple different quantiles or even fitting the entire regression quantile process. However, estimating the regression quantile process is inh...