Analysis of residuals in quantile regression: an application to income data in Brazil.

Analysis of residuals is a very important analysis usually performed in the classical regression diagnostics framework. In this paper, we propose a similar kind of analysis, but in quantile regression models. We make use of quantile residuals defined by Dunn and Smyth (1996) to verify the assumption of asymmetric Laplace distribution (Yu and Zhang, 2005) to the errors in a quantile regression model. To illustrate the method we used data from the National Household Sample Survey, performed in Brazil. We were able to visualize a better approximation of the asymmetric Laplace assumption only in the log-linear model fitted to describe income as a function of other variables