This paper introduces a new framework for quantile estimation. Quantile regression techniques have proven to be extremely valuable in understanding the relationship between explanatory variables and the conditional distribution of the outcome variable. Quantile regression allows the effect of the explanatory variables to vary based on a nonseparable disturbance term, frequently interpreted as “...

Quantile regression is used in many areas of applied research and business. Examples are actuarial, financial or biometrical applications. We show that a non-parametric generalization of quantile regression based on kernels shares with support vector machines the property of consistency to the Bayes risk. We further use this consistency to prove that the non-parametric generalization approximat...

This vignette is a slightly modified version of Koenker (2008a). It was written in plain latex not Sweave, but all data and code for the examples described in the text are available from either the JSS website or from my webpages. Quantile regression for censored survival (duration) data offers a more flexible alternative to the Cox proportional hazard model for some applications. We describe t...

We propose a notion of conditional vector quantile function and a vector quantile regression. A conditional vector quantile function (CVQF) of a random vector Y , taking values in R given covariates Z = z, taking values in R, is a map u 7→ QY |Z(u, z), which is monotone, in the sense of being a gradient of a convex function, and such that given that vector U follows a reference non-atomic distr...

Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high dimensional covariates primarily focuses on examination of model sparsity at a single or multiple quantile levels, which are typically prespecified ad hoc by the users. The resulting models may...

The composite quantile regression should provide estimation efficiency gain over a single quantile regression. In this paper, we extend composite quantile regression to nonparametric model with random censored data. The asymptotic normality of the proposed estimator is established. The proposed methods are applied to the lung cancer data. Extensive simulations are reported, showing that the pro...

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...