On the mean-shift outlier model for LAD regression

The least absolute deviation (LAD) regression technique is well known for providing an estimation mechanism insensitive to outliers in the response variable. However, relatively few studies have highlighted that these models still can be susceptible to influential observations; therefore the development of appropriate diagnostic measures is required. In this paper, we introduce a procedure for detecting outlying observations in LAD regression based on the mean-shift outlier model. This formulation provides a framework for defining standardized residuals, which enables the construction of a QQ-plot with simulated envelope. A noteworthy by-product of this work is the derivation of the gradient statistic for testing linear hypotheses in LAD regression. We illustrate our findings through the analysis of two datasets commonly examined in the literature.