THE USE AND INTERPRETATION OF RESIDUALS BASED ON ROBUST ESTIMATION

Residual plots and diagnostic techniques are important tools for exami ning the fit of a regression model. In the caw of least squares fits, plots of residuals provide a visual assessment of the adequacy of vari ous aspects of the fitted model. An important question is whether plot s of robust residuals can be interpreted in the same manner as their l east squares counterparts. This article this problem for two popular c lasses of robust estimates: M estimates and GM estimates of the Mallow s and Schweppe types. First-order properties of the residuals and fitt ed values are derived under correct and misspecified models. These pro perties are insightful on the general interpretability of robust resid ual plots and on their ability to detect curvature in misspecified mod els. The results of a simulation study consisting of tests for randomn ess and curvature in residual plots supports these theoretical propert ies. Standardization of robust residuals is also presented.