Robust quantile regression using a generalized class of skewed distributions

It is well known that the widely popular mean regression model could be inadequate if the probability distribution of the observed responses do not follow a symmetric distribution. To deal with this situation, the quantile regression turns to be a more robust alternative for accommodating outliers and the misspecification of the error distribution because it characterizes the entire conditional distribution of the outcome variable. This paper presents a likelihood‐based approach for the estimation of the regression quantiles based on a new family of skewed distributions. This family includes the skewed version of normal, Student‐ t , Laplace, contaminated normal and slash distribution, all with the zero quantile property for the error term and with a convenient and novel stochastic representation that facilitates the implementation of the expectation–maximization algorithm for maximum likelihood estimation of the p th quantile regression parameters. We evaluate the performance of the proposed expectation–maximization algorithm and the asymptotic properties of the maximum likelihood estimates through empirical experiments and application to a real‐life dataset. The algorithm is implemented in the R package lqr , providing full estimation and inference for the parameters as well as simulation envelope plots useful for assessing the goodness of fit. Copyright © 2017 John Wiley & Sons, Ltd.