Robust Quantile Regression using a Generalized Class of Skewed Distributions

Christian E. Galarza
Víctor H. Lachos
Celso R. B. Cabral
Luis M. Castro

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 since it characterizesthe 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 introduced by Wichitaksorn et al. (2014). This family includes the skewed version of Normal, Student-t, Laplace, contaminated Normal and slash distribution, all with the zeroquantile property for the error term, and with a convenient and novel stochastic representation which facilitates the implementation of the EM algorithm for maximum-likelihood estimation of the pth quantile regression parameters. We evaluate the performance of the proposed EM 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 envelopes plots useful for assessing the goodness-of-fit.

Quantile regression model
EM algorithm
Scale mixtures of Normal distributions