The ROBUSTREG procedure uses the robust multivariate location and scale estimates for leverage-point detection. The procedure computes a robust version of the Mahalanobis distance by using the minimum covariance determinant (MCD) method of Rousseeuw (1984).
Algorithm
PROC ROBUSTREG implements the algorithm given by Rousseeuw and Van Driessen (1999) for MCD, which is similar to the algorithm for LTS.
Robust Distance
The Mahalanobis distance is defined as
where 
and 
are the empirical multivariate location and scale. Here 
does not include the intercept. The relation between the Mahalanobis distance 
and the hat matrix 
is
The robust distance is defined as
where 
and 
are the robust multivariate location and scale obtained by MCD.
These distances are used to detect leverage points.
