No-crossing single-index quantile regression curve estimation

Estimation of single-index quantile regression Model

Abstract The conditional quantile function m(X) of response variable Y given the value of covariate X is modeled through a single-index model, i.e. m(X) = m(θ 0 X) for some unknown parameter vector θ0. An iterated algorithm is proposed to estimate θ0. To establish the root-n consistency of the estimator, we prove a convexity lemma for almost sure convergence, parallel to the results by Pollard ...

Noncrossing quantile regression curve estimation.

Since quantile regression curves are estimated individually, the quantile curves can cross, leading to an invalid distribution for the response. A simple constrained version of quantile regression is proposed to avoid the crossing problem for both linear and nonparametric quantile curves. A simulation study and a reanalysis of tropical cyclone intensity data shows the usefulness of the procedur...

A Single-index Quantile Regression Model and Its Estimation

Bayesian quantile regression for single-index models

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the...

Single index quantile regression for heteroscedastic data

Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. Linear and nonlinear QR models have been studied extensively, while recent research focuses on the single index quantile regression (SIQR) model. Compared to the single index mean regression problem, the fitting and the asymptotic theory of the SIQR model are more complicated due to...