Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. (2012) proposed efficient quantile regression by rounding the sharp corner of the loss. The main modification generally involves an asymmetric l2 adjustment of the loss function around zero. We ext...

Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields po...

Censored quantile regression has become an important alternative to the Cox proportional hazards model in survival analysis. In contrast to the central covariate effect from the meanbased hazard regression, quantile regression can effectively characterize the covariate effects at different quantiles of the survival time. When covariates are measured with errors, it is known that naively treatin...

The choice of a smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators. In nonparametric mean regression various methods for bandwidth selection exists. But in nonparametric quantile regression bandwidth choice is still an unsolved problem. In this paper a selection procedure for local varying bandwidths based on the asymptotic mean squared error (MSE) of ...