Regression diagnostics for rank-based methods

Residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model. In this article we explore the properties of the residuals from a rank-based fit of the model. We present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank-based fit. We show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model. Furthermore, our diagnostic techniques inherit the excellent efficiency properties of the rank-based fit over a wide class of error distributions, including asymmetric distributions. We illustrate these techniques with several examples.