Two Diagnostic Displays for Robust Regression Analysis

Abstract

We introduce a pair of displays that summarize the behavior of the regression coefficients and the corresponding residuals, that are obtained when the “trimming” parameter in Huber's family of M-estimates is allowed to vary continuously over its whole range [0, ∞], The displays exhibit the degree to which the estimates and residuals are sensitive to changes in the implicit weights attached to the worst-fitting points. They are thus effective in identifying the presence and influences of any outliers that occur in the data. They can also be used to select a single “best” set of estimates and the associated residuals.