In quantile regression of survival data, the estimation of the regression coefficients for extreme quantiles can be affected by severe censoring. Measurement error in covariates also leads to bias and loss in efficiency of estimators. In this seminar, we discuss the methodologies that effectively use the auxiliary information to improve the efficiency of censored quantile regression estimators....

Climate change may lead to changes in several aspects of the distribution of climate variables, including changes in the mean, increased variability, and severity of extreme events. In this paper, we propose using spatiotemporal quantile regression as a flexible and interpretable method for simultaneously detecting changes in several features of the distribution of climate variables. The spatio...

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 “...

Recently, quantile regression (QR) models are often applied for longitudinal data analysis. When the distribution of responses seems to be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. In this paper, a semi-parametric quantile regression model is developed for analysing continuous longitudinal responses. The error term's distribution is assumed to be Asymmetr...

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...