## Preprint 2017-06

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

### 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 since it characterizes the entire conditional distribution of the outcome variable. This paper presents a likelihoodbased 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 zero quantile 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.