Regression quantiles, along with the dual methods of regression rank scores, can be considered one of the major statistical breakthroughs of the past decades. Its advantages over the other estimation methods have been well investigated. Regression quantile methods provide a much more complete statistical analysis of the stochastic relationships among variables; in addition, they are more robust...

Estimation of reference growth curves for children's height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population. Age-specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods. Non-parametric quantile regression methods offer a complementary st...

[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...

Conventional analysis using quantile regression typically focuses on fitting the regression model at different quantiles separately. However, in situations where the quantile coefficients share some common feature, joint modeling of multiple quantiles to accommodate the commonality often leads to more efficient estimation. One example of common features is that a predictor may have a constant e...

We introduce Quantile Boost (QBoost) algorithms which predict conditional quantiles of the interested response for regression and binary classification. Quantile Boost Regression (QBR) performs gradient descent in functional space to minimize the objective function used by quantile regression (QReg). In the classification scenario, the class label is defined via a hidden variable, and the quant...

Allowing for misspecification in the linear conditional quantile function, this paper provides a new interpretation and the semiparametric efficiency bound for the quantile regression parameter β(τ) in Koenker and Bassett (1978). The first result on interpretation shows that under a mean-squared loss function, the probability limit of the Koenker–Bassett estimator minimizes a weighted distribut...

We propose both a penalized quantile regression and an independence screening procedure to identify important covariates and to exclude unimportant ones for a general class of ultrahigh dimensional single-index models, in which the conditional distribution of the response depends on the covariates via a single-index structure. We observe that the linear quantile regression yields a consistent e...

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the expected tilted loss function. The integration required in learning is not analytically tractable so to speed up the learning we employ the Expectation Propagat...

In this paper we discuss the asymptotical properties of quantile processes under random censoring. In contrast to most work in this area we prove weak convergence of an appropriately standardized quantile process under the assumption that the quantile regression model is only linear in the region, where the process is investigated. Additionally, we also discuss properties of the quantile proces...

In this paper, we develop a diagnostic procedure to assessing the homogeneity of conditional densities at a specified quantile in quantile regression estimation; this procedure is based on an asymptotic representation of the distribution of covariate values in the quantile regression basic solution.