|Robust Regression Examples|
This section is based entirely on Rousseeuw and Van Zomeren (1990). Observations , which are far away from most of the other observations, are called leverage points. One classical method inspects the Mahalanobis distances to find outliers :
Note that the MVE subroutine prints the classical Mahalanobis distances together with the robust distances . In classical linear regression, the diagonal elements of the hat matrix
The definition of a leverage point is, therefore, based entirely on the outlyingness of and is not related to the response value . By including the value in the definition, Rousseeuw and Van Zomeren (1990) distinguish between the following:
Rousseeuw and Van Zomeren (1990) propose to plot the standardized residuals of robust regression (LMS or LTS) versus the robust distances obtained from MVE. Two horizontal lines corresponding to residual values of and -2.5 are useful to distinguish between small and large residuals, and one vertical line corresponding to the is used to distinguish between small and large distances.