Robust quantile regression using a generalized class of skewed distributions

Abstract

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 pth 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.